Question

A bullet of mass M is fired with a velocity of 50 ms^-1 at an angle θwith the horizontal. At the highest point of trajectory it collides with a bob of mass 3M suspended vertically by a massless string of length 10/3m and gets embedded into it. After the collision the string moves through an angle 120⁰=, what is the angle of throw θ.

• A. cos^-1 2/5
• B. cos^-1 3/5
• C. cos^-1 4/5
• D. cos^-1 1/5

Answer 1

Answer: (C)

cos^-1 4/5

Answer 2

Velocity at highest point = u cos θ

Then Mu cos θ = (M + 3M)v

or v = $\frac { \mathrm { u } \cos \theta } { 4 }$

and 4 Mgh = $\frac { 1 } { 2 } 4 \mathrm { M } \left( \frac { \mathrm { u } \cos \theta } { 4 } \right) ^ { 2 }$

Using the given values we get

or cos² θ = $\frac { 16 } { 25 }$ or cos θ = $\frac { 4 } { 5 }$

or θ = cos^-1 $\frac { 4 } { 5 }$