Answer to Question #299880 in Physics for Hiba

Question

A ball is thrown downward from the roof of a 24 m tall building with an initial speed of 5 m/s. (a) Use energy principles to find the speed with which the ball hits the ground. (b) Find the time it took the ball to reach the ground. (c) If the ball were thrown upwards from the roof with the same speed repeat the calculations for parts (a) and (b)

Answer 1

Given:

$h=24\:\rm m$

$v_1=5\:\rm m/s$

(a) The law of conservation of energy says

$$\frac{mv_1^2}{2}+mgh=\frac{mv_2^2}{2}$$

$$v_2=\sqrt{v_1^2+2gh}=\sqrt{5^2+2*9.8*24}=22\:\rm m/s$$

(b) the time it took the ball to reach the ground

$$t=\frac{v_2-v_1}{g}=\frac{22-5}{9.8}=1.7\:\rm s$$

(c) the law of conservation of energy says

$$\frac{mv_1^2}{2}+mgh=\frac{mv_2^2}{2}$$

$$v_2=\sqrt{v_1^2+2gh}=\sqrt{5^2+2*9.8*24}=22\:\rm m/s$$

(d) the time it took the ball to reach the ground

$$t=\frac{v_2+v_1}{g}=\frac{22+5}{9.8}=2.8\:\rm s$$