Question

A cricket ball is thrown up with a speed of 19.6 m/s. The maximum height it can reach is
A. 9.8 m
B. 19.6 m
C. 29.4 m
D. 39.2 m

Answer 1

Hint: At first we need to look into the question to find the values that are given in the question, now we have to draw a pictorial representation of the question to easily solve it. Now we will have to apply the third equation of motion to get the required result.

Formula used: $2gh={{v}^{2}}-{{u}^{2}}$

Complete step by step answer:
The question is very simple to understand, let’s look at the question to find the values that are given in it,
So the ball is thrown up with a velocity of 19.6m/s.
Now, we are asked to find the maximum height that the ball can reach after throwing.

In the above diagram we can see a person throwing the ball with the velocity of 19.6 m/s, now we know that on the ball there will be a pull from the center of the earth that will attract it towards itself so, the ball will be experiencing a gradual decrease in velocity.
So, we can say that at a point the ball will be fully stationary in the air, with the velocity of 0 m / s now at this point the ball will also be at its maximum height and we are asked to find that.
So,
Initial velocity(u) = 19.6 m/s.
Final velocity (v) = 0m/s.
Acceleration due to gravity that is the gravitational pull, is $g=9.8m/{{s}^{2}}$.
Let the Height reached by the ball be h.
Now, we know that from the third equation of motion,
$2gh={{v}^{2}}-{{u}^{2}}$
$-2\times 9.8\times h={{0}^{2}}-{{(19.6)}^{2}}$,
So, now on solving this for the value of ‘h’ we get,
h = 19.6 m

So, the correct answer is “Option B”.

Note: The third equation of motion gives us the value of final velocity of an object under uniform acceleration provided that the distance travelled and the initial velocity is given. Now in the equation $2gh={{v}^{2}}-{{u}^{2}}$, ‘g’ is being used as the ball is going upwards acceleration due to gravity will enforce on the ball. ‘h’ is used instead of ‘s’, actually ‘s’ represents the horizontal distance travelled while ‘h’ represents the vertical distance travelled by the ball.