Given a light source, an object, and a wall or surface, use similar triangles and the chain rule to find the rate of change of the length of a shadow as the object moves.
A person whose height is 6 feet is walking away from the base of a streetlight along a straight path at a rate of 4 feet per second. If the height of the streetlight is 15 feet, what is the rate at which the person's shadow is lengthening? (A) $1.5 \text{ ft/sec}$ (B) $2.667 \text{ ft/sec}$ (C) $3.75 \text{ ft/sec}$ (D) $6 \text{ ft/sec}$ (E) $10 \text{ ft/sec}$
A lantern is placed on the ground 100 feet away from a wall. A man six feet tall is walking at a speed of 10 feet/second from the lantern to the nearest point on the wall. When he is midway between the lantern and the wall, the rate of change (in ft./sec.) in the length of his shadow is (A) 2.4 (B) 3 (C) 3.6 (D) 12
A lantern is placed on the ground 100 feet away from a wall. A man six feet tall is walking at a speed of 10 feet/second from the lantern to the nearest point on the wall. When he is midway between the lantern and the wall, the rate of change in the length of his shadow is (a) $3.6 \mathrm { ft } . / \mathrm { sec }$. (b) $2.4 \mathrm { ft } . / \mathrm { sec }$. (c) $3 \mathrm { ft } . / \mathrm { sec }$. (d) $12 \mathrm { ft } . / \mathrm { sec }$.
A lantern is placed on the ground 100 feet away from a wall. A man six feet tall is walking at a speed of 10 feet/second from the lantern to the nearest point on the wall. When he is midway between the lantern and the wall, the rate of change in the length of his shadow is (a) $3.6 \mathrm { ft } . / \mathrm { sec }$. (b) $2.4 \mathrm { ft } . / \mathrm { sec }$. (c) $3 \mathrm { ft } . / \mathrm { sec }$. (d) $12 \mathrm { ft } . / \mathrm { sec }$.
A lantern is placed on the ground 100 feet away from a wall. A man six feet tall is walking at a speed of 10 feet/second from the lantern to the nearest point on the wall. When he is midway between the lantern and the wall, the rate of change (in ft./sec.) in the length of his shadow is (A) 2.4 (B) 3 (C) 3.6 (D) 12
A lantern is placed on the ground 100 feet away from a wall. A man six feet tall is walking at a speed of 10 feet/second from the lantern to the nearest point on the wall. When he is midway between the lantern and the wall, the rate of change (in ft./sec.) in the length of his shadow is (A) 2.4 (B) 3 (C) 3.6 (D) 12