Question

A plank fitted with a gun is moving on a horizontal surface with speed of 4 m/s along the positive x-axis. The z-axis is in vertically upward direction. The mass of the plank including the mass of the mass of the gun is 50 kg. When the plank reaches the origin, a shell of mass 10 kg is fired at an angle of ${60}^{\circ }$ with the positive x-axis with a speed of v=20 m/s with respect to the gun n x-z plane. Find the position vector of the shell at t=2 s after firing it. Take $g=9.8m/s^2.$

• A. $[15\hat{i}-24\hat{k}]m$
• B. $[28\hat{i}+15\hat{k}]m$
• C. $[15\hat{i}-18\hat{k}]m$
• D. $[14\hat{i}-15\hat{k}]m$

Answer 1

The correct option is B $[28\hat{i}+15\hat{k}]m$

Velocity of the shell wrt to plank $v_{s,p}=20cos60\hat{i}+20sin60\hat{j}$

Actual velocity of the shell, $v_s=v_{s,p}+v_{pi}$

$v_s=14\hat{i}+10\sqrt{3}\hat{j}$

Horizontal component of position vector of shell after two seconds is given by:

$x=14\times 2=28$

Vertical component of position vector of shell after two seconds is given by:

$y=10\sqrt{3}\times 2-\frac{1}{2}\times 9.8\times 2^2\approx 15$

Hence position vector is $28\hat{i}+15\hat{j}$