Question

From a building two balls A and B are thrown such that A is thrown upwards and B downwards with the same speed (both vertically). If ${v_A}$ and ${v_B}$​ are their respective velocities on reaching the ground then,
A. ${v_B} > {v_A}$
B. ${v_B} = {v_A}$
C. ${v_A} > {v_B}$
D. their velocities depends upon their mass

Answer 1

Hint: In order to solve this question, we will sue the concept that when a body is thrown vertically with some velocity then upon its return journey due to gravity its velocity at point of projection is always same and then we will determine the relation between velocities of two balls A and B.

Formula used:
The equation of motion i.e, used here is,
${v}^2 = {u^2} + 2gH$
Here, $v$ is the final velocity, $u$ is the initial velocity and $H$ is the height that needs to be travelled.

Complete step by step solution:
Let us suppose ball A is thrown with speed u so, after reaching its maximum height ball will fall down under the effect of gravity and at the point of projection which is at the building top surface the velocity will be same as that of initial velocity which is u and body B is already thrown downwards with velocity u so now the case is both bodies A and B are falling from the building in downward direction with initial velocities u.

Now using equation of motion the final velocity of body A and B upon reaching the ground can be calculated for body A ${v_A}^2 = {u^2} + 2gH$ where v is final velocity and H is height from building top surface to ground and similarly for body B, we have ${v_B}^2 = {u^2} + 2gH$ so from both the equations we see that,
${v_A}^2 = {v_B}^2 \\
\therefore {v_A} = {v_B} \\ $
Hence, the correct answer is option B.

Note: It should be noted that, while the final velocity of both the bodies are same but both bodies will not fall on the ground at same time because body A has to cover a larger distance as it goes first upwards and then return to building top surface and again falling down towards the surface.