14. a boy throws a rock straight up with an initial speed of 8 m/s. what is the rock’s speed when he catches…

Explanation:

Step1: Analyze the motion

The rock is in free - fall motion. The acceleration due to gravity (g=- 9.8\ m/s^{2}) (taking upward as positive). The displacement (y = 0) when the boy catches the rock again. We use the kinematic equation (v^{2}=v_{0}^{2}+2ay).

Step2: Substitute values

Given (v_{0}=8\ m/s), (a=-g=- 9.8\ m/s^{2}), and (y = 0). Substitute into the equation (v^{2}=v_{0}^{2}+2ay): [ \begin{align*} v^{2}&=(8)^{2}+2\times(-9.8)\times0\ v^{2}&=64\ v&=\pm8\ m/s \end{align*} ] Since the direction is downward when caught (opposite to the initial upward direction), we take the negative value. But speed is a scalar quantity, so we take the magnitude.

Answer:

(8\ m/s)