Research shows that a driver who drives a car at a constant speed travels ``blindly'' (that is, without vision of the road) a distance proportional to the time spent looking at the cell phone while typing the message. Consider that this indeed happens. Suppose that two drivers ($X$ and $Y$) drive at the same constant speed and type the same message on their cell phones. Suppose, further, that the time spent by driver $X$ looking at his cell phone while typing the message corresponds to $25\%$ of the time spent by driver $Y$ to perform the same task.
The ratio between the distances traveled blindly by $X$ and $Y$, in that order, is equal to
(A) $\frac{5}{4}$
(B) $\frac{1}{4}$
(C) $\frac{4}{3}$
(D) $\frac{4}{1}$
(E) $\frac{3}{4}$

The result of an electoral survey, regarding voter preference in relation to two candidates, was represented by means of Graph 1. When this result was published in a newspaper, Graph 1 was cut during layout, as shown in Graph 2. Although the values presented were correct and the width of the columns was the same, many readers criticized the format of Graph 2 printed in the newspaper, claiming that there was visual harm to candidate B.
The difference between the ratios of the height of column B to column A in graphs 1 and 2 is
(A) 0
(B) $\frac{1}{2}$
(C) $\frac{1}{5}$
(D) $\frac{2}{15}$
(E) $\frac{8}{35}$

To decorate a children's party table, a chef will use a spherical melon with a diameter measuring 10 cm, which will serve as a support for inserting various candies. He will remove a spherical cap from the melon, and, to ensure the stability of this support, making it difficult for the melon to roll on the table, the chef will make the cut so that the radius $r$ of the circular section of the cut is at least 3 cm. On the other hand, the chef will want to have the largest possible area of the region where the candies will be attached.
To achieve all his objectives, the chef should cut the melon cap at a height $h$, in centimeters, equal to
(A) $5 - \frac{\sqrt{91}}{2}$
(B) $10 - \sqrt{91}$
(C) 1
(D) 4
(E) 5

How much time do you spend connected to the internet? To answer this question, a small computer application was created that runs on the desktop to automatically generate a pie chart, mapping the time a person accesses five visited websites. On a computer, it was observed that there was a significant increase in access time from Friday to Saturday on the five most accessed websites.
Analyzing the computer graphs, the highest rate of increase in access time from Friday to Saturday was on the website
(A) X.
(B) Y.
(C) Z.
(D) W.
(E) U.

A pivot with three towers ($\mathrm{T}_{1}$, $\mathrm{T}_{2}$, and $\mathrm{T}_{3}$) will be installed on a farm, with the distances between consecutive towers as well as from the base to tower $\mathrm{T}_{1}$ being equal to 50 m. The farmer intends to adjust the speeds of the towers so that the pivot completes one full rotation in 25 hours. Use 3 as an approximation for $\pi$.
To achieve his objective, the speeds of towers $\mathrm{T}_{1}$, $\mathrm{T}_{2}$, and $\mathrm{T}_{3}$ should be, in meters per hour, of
(A) 12, 24 and 36.
(B) 6, 12 and 18.
(C) 2, 4 and 6.
(D) 300, 1200 and 2700.
(E) 600, 2400 and 5400.

Two reservoirs A and B are fed by separate pumps over a period of 20 hours. The amount of water contained in each reservoir during this period can be visualized in the figure.
The number of hours in which the two reservoirs contain the same amount of water is
(A) 1.
(B) 2.
(C) 4.
(D) 5.
(E) 6.

For a Formula 1 racing season, the fuel tank capacity of each car became 100 kg of gasoline. A team chose to use gasoline with a density of 750 grams per liter, starting the race with a full tank. At the first refueling stop, a car from this team showed a reading on its onboard computer indicating the consumption of four tenths of the gasoline originally in the tank. To minimize the weight of this car and guarantee the completion of the race, the support team refueled the car with one third of what remained in the tank upon arrival at the refueling stop.
The amount of gasoline used, in liters, in the refueling was
(A) $\frac{20}{0.075}$
(B) $\frac{20}{0.75}$
(C) $\frac{20}{7.5}$
(D) $20 \times 0.075$
(E) $20 \times 0.75$

The project includes $100 \mathrm{~m}^{2}$ of solar panels that will be installed in the parking lots, producing electrical energy and providing shade for cars. On the pediatric hospital approximately $300 \mathrm{~m}^{2}$ of panels will be placed, with $100 \mathrm{~m}^{2}$ to generate electrical energy used on campus, and $200 \mathrm{~m}^{2}$ for thermal energy generation, producing water heating used in the hospital's boilers.
Suppose that each square meter of solar panel for electrical energy generates a savings of 1 kWh per day and each square meter producing thermal energy allows saving $0.7 \mathrm{~kWh}$ per day for the university. In a second phase of the project, the area covered by solar panels that generate electrical energy will be increased by 75\%. In this phase, the coverage area with panels for thermal energy generation should also be expanded.
To obtain double the amount of energy saved daily, compared to the first phase, the total area of panels that generate thermal energy, in square meters, should have a value closest to
(A) 231.
(B) 431.
(C) 472.
(D) 523.
(E) 672.

At 17:15 a heavy rain begins, falling with constant intensity. A swimming pool in the shape of a rectangular parallelepiped, which was initially empty, begins to accumulate rainwater and, at 18:00, the water level inside reaches 20 cm in height. At this instant, the valve that releases water drainage through a drain located at the bottom of this pool is opened, whose flow rate is constant. At 18:40 the rain stops and, at that exact instant, the water level in the pool dropped to 15 cm.
The instant when the water in this pool will finish draining completely is between
(A) 19:30 and 20:10.
(B) 19:20 and 19:30.
(C) 19:10 and 19:20.
(D) 19:00 and 19:10.
(E) 18:40 and 19:00.

QUESTION 103
The rumble strip is a physical device installed on the surface of a roadway so as to cause vibration and noise when a vehicle passes over it, alerting to an atypical situation ahead, such as construction, tolls, or pedestrian crossing. When passing over rumble strips, the vehicle's suspension undergoes vibrations that produce sound waves, resulting in a peculiar noise. Consider a vehicle that passes with constant velocity equal to $108 \frac{\mathrm{~km}}{\mathrm{~h}}$ over a rumble strip whose strips are separated by a distance of 8 cm.
Available at: \href{http://www.denatran.gov.br}{www.denatran.gov.br}. Accessed on: 2 Sep. 2015 (adapted).
The frequency of the vehicle's vibration perceived by the driver during passage over this rumble strip is closest to
(A) 8.6 hertz.
(B) 13.5 hertz.
(C) 375 hertz.
(D) 1350 hertz.
(E) 4860 hertz.

QUESTION 104
People who use objects whose operating principle is the same as that of levers apply a force, called the effort force, at a given point on the bar, to overcome or balance a second force, called the load force, at another point on the bar. Because of the different distances between the points of application of the effort and load forces, their effects are also different. The figure shows some examples of these objects.
[Figure]
In which of the objects is the effort force greater than the load force?
(A) Tweezers.
(B) Pliers.
(C) Nutcracker.
(D) Wheelbarrow.
(E) Bottle opener.

QUESTION 108
While researching a resistor made of a new type of material, a scientist observed the behavior shown in the voltage versus current graph.
[Figure]
After analyzing the graph, he concluded that the voltage as a function of current is given by the equation $\mathrm{V} = 10i + i^{2}$. The graph of the electrical resistance $(R)$ of the resistor as a function of current (i) is
(A) [Figure]
(B) [Figure]
(C) [Figure]
(D) [Figure]
(E) [Figure]

QUESTION 112
Many smartphones and tablets no longer need keys, since all commands can be given by pressing the screen itself. Initially this technology was provided through resistive screens, formed basically by two layers of transparent conductive material that do not touch until someone presses them, modifying the total resistance of the circuit according to the point where the touch occurs. The image is a simplification of the circuit formed by the plates, in which A and B represent points where the circuit can be closed by means of touch.
[Figure] [Figure]
What is the equivalent resistance in the circuit caused by a touch that closes the circuit at point $\mathbf{A}$?
(A) $1.3 \mathrm{~k}\Omega$
(B) $4.0 \mathrm{~k}\Omega$
(C) $6.0 \mathrm{~k}\Omega$
(D) $6.7 \mathrm{~k}\Omega$
(E) $12.0 \mathrm{~k}\Omega$

QUESTION 136
A person needs to travel from city A to city B. There are two possible routes: route 1, with a length of 200 km, and route 2, with a length of 240 km. The person travels route 1 at an average speed of 80 km/h and route 2 at an average speed of 100 km/h.
Which route takes less time, and what is the difference in travel time between the two routes?
(A) Route 1, with a difference of 6 minutes. (B) Route 1, with a difference of 12 minutes. (C) Route 2, with a difference of 6 minutes. (D) Route 2, with a difference of 12 minutes. (E) Both routes take the same time.

The objective of thermal insulating containers is to minimize heat exchange with the external environment. This heat exchange is proportional to the thermal conductivity k and the internal area of the container's faces, as well as to the difference in temperature between the external environment and the interior of the container, in addition to being inversely proportional to the thickness of the faces.
In order to evaluate the quality of two containers A ($40 \mathrm{~cm} \times 40 \mathrm{~cm} \times 40 \mathrm{~cm}$) and B ($60 \mathrm{~cm} \times 40 \mathrm{~cm} \times 40 \mathrm{~cm}$), with faces of the same thickness, a student compares their thermal conductivities $\mathrm{k}_{\mathrm{A}}$ and $\mathrm{k}_{\mathrm{B}}$. To do this, she suspends identical blocks of ice at $0^{\circ}\mathrm{C}$ inside each container, so that their surfaces are in contact only with air. After a time interval, she opens the containers while both still contain some ice and verifies that the mass of ice that melted in container $\mathbf{B}$ was twice that which melted in container $\mathbf{A}$.
The ratio $\frac{k_{A}}{k_{B}}$ is closest to
(A) 0.50.
(B) 0.67.
(C) 0.75.
(D) 1.33.
(E) 2.00.

Slackline is a sport in which the athlete must balance and perform maneuvers while standing on a stretched ribbon. For the practice of the sport, the two ends of the ribbon are fixed so that it is a few centimeters from the ground. When an athlete with a mass equal to 80 kg is exactly in the middle of the ribbon, it moves vertically, forming an angle of $10^{\circ}$ with the horizontal, as shown in the figure. It is known that the acceleration due to gravity is equal to $10 \mathrm{~m~s}^{-2}$, $\cos\left(10^{\circ}\right) = 0.98$ and $\sin\left(10^{\circ}\right) = 0.17$.
What is the force that the ribbon exerts on each of the trees because of the presence of the athlete?
(A) $4.0 \times 10^{2} \mathrm{~N}$
(B) $4.1 \times 10^{2} \mathrm{~N}$
(C) $8.0 \times 10^{2} \mathrm{~N}$
(D) $2.4 \times 10^{3} \mathrm{~N}$
(E) $4.7 \times 10^{3} \mathrm{~N}$

In any civil construction work, the use of personal protective equipment, such as helmets, is fundamental. For example, the free fall of a brick with mass $2.5 \mathrm{~kg}$ from a height of 5 m, whose impact against a helmet can last up to $0.5 \mathrm{~s}$, results in an average impulsive force greater than the weight of the brick. Assume that the gravitational acceleration is $10 \mathrm{~m~s}^{-2}$ and that the effect of air resistance is negligible.
The average impulsive force generated by this impact is equivalent to the weight of how many equal bricks?
(A) 2
(B) 5
(C) 10
(D) 20
(E) 50

A diver becomes trapped while exploring a cave in the ocean. Inside the cave an air pocket formed, as shown in the figure, where the diver took shelter.
During the rescue, to prevent damage to his body, it was necessary for the diver to undergo a decompression process before returning to the surface so that his body would be under atmospheric pressure again. The graph shows the relationship between the recommended decompression times for individuals in this situation and the pressure variation.
Consider that the acceleration due to gravity is equal to $10\mathrm{~m~s^{-2}}$ and that the density of water is $\rho = 1000\mathrm{~kg~m^{-3}}$. In minutes, what is the decompression time to which the diver should be subjected?
(A) 100
(B) 80
(C) 60
(D) 40
(E) 20

The Eiffel Tower, with its 324 meters of height, made with iron trusses, weighed 7300 tons when it finished being built in 1889. An architect decides to build a prototype of this tower on a 1:100 scale, using the same materials (each linear dimension on a 1:100 scale of the real monument). Consider that the real tower has a mass $\mathrm{M}_{\text{tower}}$ and exerts on the foundation upon which it was erected a pressure $\mathrm{P}_{\text{tower}}$. The model built by the architect will have a mass $\mathrm{M}_{\text{model}}$ and will exert a pressure $\mathrm{P}_{\text{model}}$.
How does the pressure exerted by the tower compare with the pressure exerted by the prototype? That is, what is the ratio between the pressures $(\mathrm{P}_{\text{tower}})/(\mathrm{P}_{\text{model}})$?
(A) $10^{0}$
(B) $10^{1}$
(C) $10^{2}$
(D) $10^{4}$
(E) $10^{6}$

Two engineers are verifying whether a cavity drilled in the ground is in accordance with the planning of a construction project, whose required depth is 30 m. The test is performed by a device called a variable frequency audio oscillator, which allows relating the depth with the values of the frequency of two consecutive resonances, just as in a closed sound tube. The lowest resonance frequency that the device measured was 135 Hz. Consider that the speed of sound inside the drilled cavity is $360\mathrm{~m~s^{-1}}$.
If the depth is in accordance with the project, what will be the value of the next resonance frequency that will be measured?
(A) 137 Hz.
(B) 138 Hz.
(C) 141 Hz.
(D) 144 Hz.
(E) 159 Hz.

The obtaining of ethanol using sugarcane involves the fermentation of monosaccharides that form the sucrose contained in molasses. One of these formers is glucose $\left(\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6\right)$, whose fermentation produces about 50 g of ethanol from 100 g of glucose, according to the chemical equation described.
Under a specific fermentation condition, 80\% conversion to ethanol is obtained which, after its purification, presents a density equal to $0.80 \mathrm{~g/mL}$. The molasses used contained 50 kg of monosaccharides in the form of glucose.
The volume of ethanol, in liters, obtained in this process is closest to
(A) 16.
(B) 20.
(C) 25.
(D) 64.
(E) 100.

Analyzing the technical sheet of a popular automobile, some characteristics are verified in relation to its performance. Considering the same automobile in two versions, one of them running on alcohol and another on gasoline, we have the data presented in the table, in relation to the performance of each engine.

Parameter	Gasoline engine	Alcohol engine
Acceleration	from 0 to $100 \mathrm{~km/h}$ in $13.4 \mathrm{~s}$	from 0 to $100 \mathrm{~km/h}$ in $12.9 \mathrm{~s}$
Maximum speed	$165 \mathrm{~km/h}$	$163 \mathrm{~km/h}$

Considering air resistance negligible, which version presents the greatest power?
(A) Since the gasoline version achieves the greatest acceleration, this is the one that develops the greatest power.
(B) Since the gasoline version reaches the greatest value of kinetic energy, this is the one that develops the greatest power.
(C) Since the alcohol version presents the greatest rate of change of kinetic energy, this is the one that develops the greatest power.
(D) Since both versions present the same change in velocity in the acceleration calculation, the power developed is the same.
(E) Since the gasoline version keeps the engine working for more time to reach 100 km/h, this is the one that develops the greatest power.

Scientists from the University of New South Wales, in Australia, demonstrated in 2012 that Ohm's Law is valid even for very thin wires, whose cross-sectional area comprises only a few atoms. The table presents the areas and lengths of some of the constructed wires (respectively with the same units of measurement). Consider that resistivity remains constant for all geometries (an approximation confirmed by the study).

	Area	Length	Electrical resistance
Wire 1	9	312	R1
Wire 2	4	47	R2
Wire 3	2	54	R3
Wire 4	1	106	R4

The electrical resistances of the wires, in increasing order, are
(A) $\mathrm{R}1 < \mathrm{R}2 < \mathrm{R}3 < \mathrm{R}4$.
(B) $\mathrm{R}2 < \mathrm{R}1 < \mathrm{R}3 < \mathrm{R}4$.
(C) $\mathrm{R}2 < \mathrm{R}3 < \mathrm{R}1 < \mathrm{R}4$.
(D) $\mathrm{R}4 < \mathrm{R}1 < \mathrm{R}3 < \mathrm{R}2$.
(E) $\mathrm{R}4 < \mathrm{R}3 < \mathrm{R}2 < \mathrm{R}1$.

At a racetrack, cars can skid on a curve and hit the protective wall. To reduce the impact of a collision, a tire barrier can be placed on the wall, which makes the collision last longer and the car return with reduced velocity. Another option is to place a barrier made of blocks of a material that deforms, making it as long-lasting as the collision with tires, but which does not allow the car to return after the collision. Comparing the two situations, how do the average force exerted on the car and the dissipated mechanical energy compare?
(A) The force is greater in the collision with the tire barrier, and the energy dissipated is greater in the collision with the block barrier.
(B) The force is greater in the collision with the block barrier, and the energy dissipated is greater in the collision with the tire barrier.
(C) The force is greater in the collision with the block barrier, and the energy dissipated is the same in both situations.
(D) The force is greater in the collision with the tire barrier, and the energy dissipated is greater in the collision with the tire barrier.
(E) The force is greater in the collision with the block barrier, and the energy dissipated is greater in the collision with the block barrier.

The sound signal from the fall of a large block of ice from a glacier is detected by two devices located on a boat, with detector A immersed in water and B on the bow of the vessel. It is known that the speed of sound in water is $1540 \frac{\mathrm{~m}}{\mathrm{~s}}$ and in air is $340 \frac{\mathrm{~m}}{\mathrm{~s}}$.
The graphs indicate, in real time, the sound signal detected by the two devices, which were turned on simultaneously at an instant before the ice block fell. By comparing corresponding points of this signal in each device, it is possible to obtain information about the sound wave.
The distance L, in meters, between the boat and the glacier is closest to
(A) 339000.
(B) 78900.
(C) 14400.
(D) 5240.
(E) 100.