Question

A small box is connected to one end of a massless spring of un-stretched length $4.9m$. The other end of the spring is fixed. The system lies on a horizontal frictionless surface. The block is stretched by $0.2m$ and released from rest at $t=0$. It then executes simple harmonic motion with angular frequency $\omega =\frac{\pi }{3}rad/s$. Simultaneously at $t=0$, a small pebble is projected with speed $v$ from point $P$ at an angle of ${45}^{\circ }$ as shown in the figure. Point $P$ is a a horizontal distance of $10m$ from $O$. If the pebble hits the block at $t=1sec$, the value of $v$ is (take $g=10m/s^2$)

• A. $\sqrt{50}m/s$
• B. $\sqrt{51}m/s$ b
• C. $\sqrt{52}m/s$
• D. $\sqrt{53}m/s$

Answer 1

The correct option is A $\sqrt{50}m/s$

When the stone hits the unstretched spring.

Distance travelled by people = distance travelled by block

$Sp=4.9+.2\cos \omega t=4.9+.2\omega \frac{\pi }{3}=5m$

$Sp=10-hasrange=10-\frac{V^2\sin 2\theta }{g}$

$=10-\frac{V^2}{10}$

$5=10-\frac{V^2}{10}$

$V^2=50\Rightarrow V=\sqrt{50}m/s.$