Question

Two stones are thrown from the top of a tower, one straight down with an initial speed $u$ and the second straight up with the same speed $u$. When the two stones hit the ground, they will have speeds in the ratio

• A. $2:3$
• B. $2:1$
• C. $1:2$
• D. $1:1$

Answer 1

The correct option is D $1:1$

In case of stone thrown downwards, initial velocity,$u=u$
So, using equation $v^2-u^2=2aS$,
here, $u=u,v=0,a=a,S=Distance$
So, final equation$=u^2=2aS......\left(1\right)$
Again, for stone thrown upwards, initial velocity,$u=-u$
So, using equation $v^2-u^2=2aS$,
here, $u=-u,v=0,a=a,S=Distance=S$
So, final equation$=u^2=2aS.......\left(2\right)$
Dividing $\left(1\right)$ by $2,$ we get ratio of $1:1$
In both the cases$,(u$ is positive or negative$)u^2$ is positive.