Question

Elon wants to know how high he can throw a baseball vertically into the sky. He just threw the baseball up and after 4 seconds he caught it at the same height from which he threw it. If we assume there is no wind and no air resistance, determine the maximum height of the ball, and the velocity at which the ball hit his hand.

Answer 1

$\bigstar\huge\underline{\mathtt{Solution :}}$

Ball is moving upwards

• Velocity of the baseball at maximum height(v) = 0 m/s

• Acceleration due to gravity(g) = - 10 m/s ²

( as the ball is moving against gravity )

time of ascent = time of descent = t

Total time(T) = t +t

T = 2t

t = 2 sec

• Time taken by the ball to reach the maximum height = 2 sec

Let us first find the initial velocity of the ball

As the body moves with uniform acceleration throughout it's motion we can use kinematic equation in order to solve such problems

By applying first equation of motion ,

➽ v = u + gt

➽ 0 = u +(-10) x2

➽ u = 20 m /s

Now that we have the value of u let's let's find the maximum height of the ball by using the third kinematic equation

➽ v² = u² + 2gh

➽ 0  = 400 + 2  (-10)  h

➽ h = 400 / 20

➽ h = 20 m

The maximum height of the ball = 20 m

Ball is moving downwards

• Time taken by the ball to reach elon's hand (t)= 2 sec

• Velocity of the baseball at maximum height(u ') = 0 m/s

• Acceleration due to gravity(g) = +10 m/s ²

( as the ball is moving along gravity )

We need to find the velocity (v') of the ball with which the ball hit elon's hand in order to do that simply apply first equation of motion

➽ v' = u' + at

➽ v '= 0 + 10 x 2

➽ v ' = 20 m /s

The velocity of the ball with which the ball hit's elon's hand is 20 m/s