Answer to Question #161242 in Mechanics | Relativity for Chan

Question

a ball is thrown vertically upward lands on the thrower's hand in 24.5 s. find (a) the time taken by the ball to reach its maximum height, (b) the maximum height attained by the ball, and (c) the initial velocity of the ball

Answer 1

a) We can find the time taken by the ball to reach its maximum height from the formula:

$$t_{rise}=\dfrac{t}{2}=\dfrac{24.5\ s}{2}=12.25\ s.$$

b) Let's first find the initial velocity of the ball:

$$v=v_0-gt_{rise},$$ $$0=v_0-gt_{rise},$$ $$v_0=gt_{rise}=9.8\ \dfrac{m}{s^2}\cdot12.25\ s=120.05\ \dfrac{m}{s}.$$

c) Finally, we can find the maximum height attained by the ball:

$$y_{max}=v_0t_{rise}-\dfrac{1}{2}gt_{rise}^2,$$ $$y_{max}=120.05\ \dfrac{m}{s}\cdot12.25\ s-\dfrac{1}{2}\cdot9.8\ \dfrac{m}{s^2}\cdot(12.25\ s)^2=735.3\ m.$$