Question

A particle is thrown with velocity of $u$m/s. it passes $A$ and $B$ as shown in the figure at time $t_1=1s$ and $t_2=3s$. The value of $u$ is $(g=10m/s^2)$

• A. 20 m/s
• B. 10 m/s
• C. 5 m/s
• D. 40 m/s

Answer 1

The correct option is A 20 m/s

Suppose the height travelled by ball in time

$t_1$ & $t_2$ is 'h' and speed of projection is U.

Then using relation

$S=Ut+1/2a{t}^2$

$h=U{t}_1-\frac{1}{2}g{t}_1^2$ __ (1)

$h=U{t}_2-\frac{1}{2}g{t}_2^2$ __ (2)

so equating both equations

$U{t}_1-\frac{1}{2}g{t}_1^2=U{t}_2-\frac{1}{2}g{t}_2^2$

solving above we get

$U=\frac{g(t_1^2-t_2^2)}{2(t_1-t_2)}=g\frac{(t_1+t_2)}{2}$

So, $U=\frac{10(1+3)}{2}$

$U=20m/s$