Question

A bullet of mass M fired with a velocity of 50 ms^-1 at an angle θ with the horizontal. At the highest point of its trajectory, it collides head on with a bob of mass 3M suspended by a massless string of length 10/3 m and gets embedded in the bob. After the collision the string moves through the angle of 120º, find (i) The angle θ and (ii) the vertical and horizontal co-ordinates of the initial position of the bob w.r.t. the point of firing of the bullet (g = 10 ms^-2).

Answer 1

The horizontal component of the velocity of the bullet = 50 cosθ ms^-1 when the bullet strikes to bob at highest point of its trajectory.

M(50 cosθ) = (3M + M)v, where v is the velocity of the bob and bullet system,

v = 25/2 cosθ ms^-1

The length of string = 10/3 m

The vertical displacement h of the bob

= [10/3 + 10/3 sinθ] = 5 m

Now, applying the law of conservation of energy, we get

or cosθ = 5.θ = cos^-1(0.8)

Thus, the absolute of the initial position of the bob, x

= 1/2 (Range of the bullet)

And, the ordinate