Question

A ball is thrown vertically upward with a speed of 7.1 m/s. Find:

(9 points)

a. Maximum height reached the ball

b. Its time of flight

c. Velocity the ball would return to its starting point

Answer 1

$$v(t)=v_0-gt$$

$$h(t)=h_0+v_0t-\dfrac{gt^2}{2}$$

a. The ball reaches a maximum height at

$$t_1=\dfrac{v_0}{g}$$

$$h_{max}=h_0+\dfrac{v_0^2}{2g}$$

Given $h_0=0m, v_0=7.1m/s, g=9.81m/s^2$

$$h_{max}=0m+\dfrac{(7.1m/s)^2}{2(9.81m/s^2)}=2.569m$$

b.

$$t_{flight}=2t_1=\dfrac{2v_0}{g}$$

$$t_{flight}=\dfrac{2(7.1m/s)}{9.81m/s^2}=1.4475s$$

c.

$$v_{return}=v_0-gt_{flight}=-v_0$$

$$v_{return}=-7.1m/s$$