Question

If collision is perfectly inelastic then, what maximum height (from ground) will the combined mass rise?

• A. 25 m
• B. 18 m
• C. 15 m
• D. 20 m

Answer 1

Answer: (C)

15 m

Let the collision take place at $t$ sec and $s_1$ and $s_2$ be the distance traveled by the masses just before collision.
Thus we get:
$-s_1=-\frac{1}{2}g{t}^2$ and $s_2=20t-\frac{1}{2}g{t}^2$

Thus we get:

$s_1+s_2=20t$
$\Rightarrow t=1sec$

Thus, $s_2=20\left(1\right)-\frac{1}{2}10(1{)}^2=15m$

Now we will calculate the velocity of the masses just before collision
$v_1=0-gt=-10m/s$ and $v_2=20-gt=10m/s$

Now as the collision is inelastic, we have
$m{v}_1+m{v}_2=(m+m)v$

Thus we get the velocity of the combined mass as $0$.
Thus we see that the combined mass does not have any velocity and it would start falling downwards after the collision. Thus the maximum height reached is $15m$.