The co-ordinates of a particle moving in $x - y$ plane are given by : $x = 2 + 4 \mathrm { t } , y = 3 \mathrm { t } + 8 \mathrm { t } ^ { 2 }$. The motion of the particle is :
(1) uniformly accelerated having motion along a parabolic path.
(2) uniform motion along a straight line.
(3) uniformly accelerated having motion along a straight line.
(4) non-uniformly accelerated.

Q4. The co-ordinates of a particle moving in $x - y$ plane are given by : $x = 2 + 4 \mathrm { t } , y = 3 \mathrm { t } + 8 \mathrm { t } ^ { 2 }$. The motion of the particle is :
(1) uniformly accelerated having motion along a
(2) uniform motion along a straight line. parabolic path.
(3) uniformly accelerated having motion along a
(4) non-uniformly accelerated. straight line.

A particle is projected from the ground with an initial velocity making an angle of $60 ^ { \circ }$ with the horizontal. If its kinetic energy at the point of projection is $\mathrm { k } _ { 0 }$ and the kinetic energy at the highest point of the trajectory is $k _ { 1 }$, then find the value of $\frac { k _ { 0 } - k _ { 1 } } { k _ { 0 } }$\ (A) $\frac { 1 } { 2 }$\ (B) $\frac { 2 } { 3 }$\ (c) $\frac { 3 } { 4 }$\ (D) $\frac { 1 } { 5 }$

A particle is projected with an initial velocity at an angle of $45 ^ { \circ }$ to the horizontal. It reaches its maximum height at $\mathrm { t } = 2 \mathrm {~s}$ and passes the top of a building at $\mathrm { t } = 3 \mathrm {~s}$ after projection. Find the height of the building.
(A) 10 m
(B) 15 m
(C) 20 m
(D) 25 m

5. A red flag and a white flag are placed in a plaza, and Xiaoming stands between them. Using instruments on hand, Xiaoming measures that his distance to the red flag due east is 6 times his distance to the white flag due west. After walking 10 meters due north and measuring again, he finds that his distance to the red flag is now 4 times his distance to the white flag. What is the distance between the red and white flags closest to?
(1) 60 meters
(2) 65 meters
(3) 70 meters
(4) 75 meters
(5) 80 meters

II. Multiple-Choice Questions (35 points)

Instructions: For questions 6 through 12, each of the five options is independent, and at least one option is correct. Select all correct options and mark them on the ``Answer Sheet''. No deductions are made for incorrect answers. Five points are awarded for all five options correct; 2.5 points for one incorrect option; no points for two or more incorrect options.

There are two tall buildings on the ground, Building A and Building B. It is known that Building A is taller than Building B, and the horizontal distance between the two buildings is 150 meters. A person pulls a rope from the top of Building A to the top of Building B, and measures the angle of depression to the top of Building B from the top of Building A as $22^{\circ}$. Assuming the rope is pulled straight, which of the following options is closest to the length of the rope (unit: meters)? (Note: The angle of depression is the angle between the line of sight and the horizontal line when looking down at an object)
(1) $150$ (2) $150 \sin 22^{\circ}$ (3) $150 \cos 22^{\circ}$ (4) $\frac{150}{\cos 22^{\circ}}$ (5) $\frac{150}{\sin 22^{\circ}}$