Question

From the top of a tower $36$ m high, a body is dropped and at the same time another body is projected vertically upward from the ground. If they meet midway, find the initial velocity of the projected body and its velocity when the two bodies come together

• A. $5\sqrt{6}m,0m/s$
• B. $\frac{42}{\sqrt{5}}m,0m/s$
• C. $6\sqrt{6}m,2m/s$
• D. $8\sqrt{6}m,4.5m/s$

Answer 1

The correct option is B $\frac{42}{\sqrt{5}}m,0m/s$

Equation to use :

for first body $x=\frac{1}{2}g{t}^2$
for second body $(h-x)=ut-\frac{1}{2}g{t}^2$

Now solving,

For A $\Rightarrow 18=\frac{1}{2}g{t}^2$
$\sqrt{\frac{2\times 18}{g}}=t_1$

For B $\Rightarrow 18=ut-\frac{1}{2}g{t}^2(t=t_1)$
$\Rightarrow 18=u\sqrt{\frac{36}{g}}-\frac{g}{2}\times \frac{36}{g}\Rightarrow 36=u\sqrt{\frac{36}{g}}$
$\Rightarrow u=18.78=\frac{42}{\sqrt{5}}m/s$

When they come in contact:
Velocity of B is, $v_B=u-gt$ $=\frac{42}{55}-9.8\times 1.916$
$v_B=0m/s$