Question

Two balls A and B of same masses are thrown from the top of the building. A, thrown upward with velocity \[u\] and B, thrown downward with velocity $u$, then
A. Velocity of A is more than B at the ground
B. Velocity of B is more than A at the ground
C. Both A & B strike the ground with same velocity
D. None of these

Answer 1

Hint:In this question, we are given that there are two balls of same mass and same velocity are thrown from the top of the building but first one thrown in the upward direction and the other one in the other direction. We Have to find the relation between their velocities. Apply the third equation of motion and put the given values to calculate the velocity.


Formula used:

Third equation of the motion –
${v^2} = {u^2} + 2gh$
Here, $v = $ final velocity of the body
$u = $ initial velocity
$g = $ acceleration due to the gravity
$h = $ height



Complete answer:
Let, the height of the building be $h$ and the masses of the balls be $m$
Given that,
Initial speed of the ball A $ = v$
Initial velocity of the ball B $ = - v$
Here, ball are moving in upward and backward direction. So, for the backward direction assume the initial velocity to be negative.
Both balls are moving under the same acceleration. Assume it to be acceleration due to the gravity.
Let, the final velocity of ball A and B be ${v_A}$ and ${v_B}$ respectively.
Using the third equation of the motion i.e., ${v^2} = {u^2} + 2gh$
Substituting the required values,
For Ball A,
${v_A}^2 = {v^2} + 2gh$
On solving, we get ${v_A} = \sqrt {{v^2} + 2gh} $
For Ball B,
${v_B}^2 = {\left( { - v} \right)^2} + 2gh$
On solving, we get ${v_A} = \sqrt {{v^2} + 2gh} $
Thus, ${v_A} = {v_B}$
Hence, option (C) is the correct answer i.e., Both A & B strike the ground with same velocity.





Note:The phrases velocity and speed describe how fast or slow an object moves. We frequently encounter circumstances in which we must determine which of two or more things is travelling faster. If they are travelling in the same direction on the same road, it is easy to identify who is going faster. However, determining who is the fastest is difficult if their motions are in opposite directions. In such instances, the concept of velocity comes in handy.