Question

A person is throwing two balls in the air one after the other. He throws the second ball when the first ball is at the highest point. If he is throwing the balls every second, how high do they rise?
A) 5m
B) 3.75m
C) 2.50m
D) 1.25m

Answer 1

Hint: Given that the balls are thrown in an upward direction in the air, so it is an example of objects falling freely under the effect of gravity. Their initial velocity is in an upward direction. Freefall of objects is a case of motion where the acceleration is always constant. This is because the acceleration due to gravity is always constant and downwards.

Complete step by step solution:
Step I:
When the object is falling freely under influence of gravity then the shape, size, or weight of the objects are not considered. Given the ball is thrown upward, let its initial velocity is = $u$
Also, acceleration is due to gravity, $a=-g$
Time, $t = 1 sec$
Step II:
The object is falling freely and its position is changing, so the equation of motion will be used here. Equation of motion is the equation that describes the behavior of how a system is moving or changing its position with respect to time.
Using equation of motion \[v = u + at\]---(i)
Substituting values of u,v and t and solving equation (i)
\[0 = u - (g \times 1)\]
\[0 = u - g\]
\[u = g\]---(ii)
Initial velocity is equal to force due to gravity.
Step III:
Distance traveled in one second is the maximum height covered by the ball.
Using distance formula\[S = ut + \dfrac{1}{2}a{t^2}\]
\[S = g(1) + \dfrac{1}{2} \times ( - g) \times {(1)^2}\]
\[S = g - \dfrac{g}{2}\]
Solving the above equation,
\[S = \dfrac{g}{2}\]
Step IV:
Substitute the standard value of $g=10$ and evaluating the value of $S$.
\[S = \dfrac{{10}}{2} = 5m\]

$\therefore $ The distance covered by the balls is = 5m. Option A is the correct answer.

Note:
The concept of free fall was founded by Galileo. He observed that when an object is thrown upwards, there are two forces acting on it. One is the gravitational force that is trying to pull it towards the centre of Earth and one is an upward force exerted by air. It is the force applied by air on the object that opposes its motion. But the value of acceleration due to gravity remains constant, which varies according to the different locations of the Earth. When the ball is thrown upwards, at the highest point the vertical component of its velocity will be zero. Hence velocity will also be zero.