Question

At time t = 0 a ball is thrown upward from the ground with an

initial velocity of 30 m/s.
How long does it take to reach its greatest height
(apex)?
What is the greatest height reached by the
ball?

Answer 1

The time taken to reach the greatest height (apex) is approximately 3.06 seconds. The greatest height reached by the ball is approximately 46.55 meters.

Step-by-step explanation:

To find the time taken to reach the greatest height (apex), we need to consider the motion of the ball in the vertical direction. Since it is thrown upward with an initial velocity of 30 m/s, we can use the kinematic equation:

1. v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

At the apex, the final velocity is 0 m/s, the initial velocity is 30 m/s, and the acceleration is due to gravity (-9.8 m/s² since it is against the upward motion). Thus, the equation becomes:

1. 0 = 30 + (-9.8)t

Solving for t gives us the time taken to reach the apex: t ≈ 3.06 seconds.

To find the greatest height reached by the ball, we can use the equation for displacement in the vertical direction:

1. s = ut + ½at², where s is the displacement.

Substituting the values, we have:

1. s = 30(3.06) + ½(-9.8)(3.06)²

Simplifying the equation gives us the greatest height reached by the ball: ∼ 46.55 meters.