A boy kicks a football with a certain initial velocity at an angle 20° above the horizontal. In 2.0 seconds, the ball reaches at its highest point in its trajectory. What is the initial velocity of the ball?
A) 9.8 m/s
B) 20 m/s
C) 57 m/s
D) 4.9 m/s
E) 29 m/s

Question

Quizplus · Accepted Answer

Using kinematic equations, we know that the time it takes for an object to reach its highest point in its trajectory is given by:
t = (Vy_f - Vy_i) / g
where t = 2.0 seconds, Vy_f = 0 m/s (at the highest point, the vertical velocity is zero), Vy_i = V0 sin(20°) (initial vertical velocity), and g = 9.8 m/s^2 (acceleration due to gravity). 
Solving for V0, we get:
V0 = Vy_i / sin(20°) = (g*t)/sin(20°) = (9.8 m/s^2 * 2.0 s) / sin(20°) ≈ 57 m/s. 
Therefore, the initial velocity of the ball was 57 m/s.

A Boy Kicks a Football with a Certain Initial Velocity