Question

A wooden block of mass 10 g is dropped from the top of a cliff 100 m high. Simultaneously, a bullet of mass 10 g is fired from the foot of the cliffupward with a velocity of $100m{s}^{-1}$. At what time will the bullet and the block meet ?

• A. $4s$
• B. $3s$
• C. $2s$
• D. $1s$

Answer 1

The correct option is D $1s$

Height of the tower $=s_1+s_2=100m$.
Where $s_1$ and $s_2$ are the displacements covered by wooden block and bullet respectively before the collision.
For the block :
$s_1=\frac{1}{2}g{t}^2=\frac{1}{2}\times 9.8\times t^2=4.9t^2$
For the bullet :
$s_2=ut-\frac{1}{2}g{t}^2$
$=100t-\frac{1}{2}\times 9.8\times t^2=100t-4.9t^2$
Since, $s_1+s_2=100m$
$4.9t^2+100t-4.9t^2=100$
$\Rightarrow$ 100t = 100
$\Rightarrow$ t = 1s.