Question

The ratio of magnitude of velocity of projection in the upward motion to the magnitude of velocity of the body on reaching the point of projection in its downward motion is_____ .

• A. 9 : 1
• B. 1 : 1
• C. 2 : 1
• D. 4 :1

Answer 1

The correct option is B 1 : 1

At the same horizontal level, the velocities of an object thrown up have equal magnitude but are opposite in direction. Thus the ratio is $1:1$

Let us assume an object was thrown up with a velocity $u_1$ and it reaches a height $h.$ Its final velocity $v_1=0.$

Using third equation of motion,

$v_1^2-u_1^2=2(-g)h$

$u_1^2=2gh\Rightarrow u_1=\sqrt{2gh}$ upwards

Now it comes down again through the same height $h$. Let us assume its final velocity is $v_2.$ We know its initial velocity for the descend will be $u_2=0$

$v_2^2-u_2^2=2(-g)(-h)$

$v_2^2=2gh\Rightarrow v_2=\sqrt{2gh}$ downwards

So we see that the magnitude of $u_1$ and $v_2$ is same.