Question

A block of mass 5 kg moves up on a smooth inclined plane with a velocity of 10 m/s in the direction shown. A bullet of mass 60 g travelling at 500 m/s strikes the block centrally and gets embedded in it. The velocity of the block and embedded bullet in m/s immediately after the impact is

• A. 12.34 at 30${}^{\circ }$
• B. 13.84 at 51.78${}^{\circ }$
• C. 13.84 at 30 ${}^{\circ }$
• D. 15.62 at 78 ${}^{\circ }$

Answer 1

The correct option is B 13.84 at 51.78${}^{\circ }$

Using conservation of linear momentum in Y -direction

$0.06\times 500+5\times 10\sin 30=(0.06+5)\times V_y$

$V_y=10.86m/s$

Using conservation of linear momentum in X -direction

$0+\cos 30\times 5\times 10=5.06\times V_x$

$V_x=8.56m/s$

$V=\sqrt{V_x^2+V_y^2}=13.84m/s$

$\tan \theta =\frac{V_y}{V_x}$

$\theta ={51.78}^{\circ }$