Question

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

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

Answer 1

Answer: (A)

$\sqrt{50}m/s$

Correct option is A.

Time of flight for projectile:

$T=\frac{2vsin\theta }{g}$

Rearranging the formula , we get

$V=\frac{T\times g}{2sin\theta }$

Substituting the values,

$V=\frac{1\times 10}{2\times sin45}$

$V=\frac{1\times 10}{2\times \frac{1}{\sqrt{2}}}$

$V=\frac{10}{\sqrt{2}}$

$V=\sqrt{50}m{s}^{-1}.$