5. A 30.0-g rifle bullet traveling 185 m/s embeds itself in a 3.15-kg pendulum hanging on a 2.85-m-long string, which makes the pendulum swing upward in an arc. Determine: a. The vertical component of the pendulum’s maximum displacement. (10pts) b. The horizontal component of the pendulum’s maximum displacement. (10pts) c. The angle of the pendulum’s maximum displacement with the vertical. (10pts)

Explanation:

We shall apply law of conservation of momentum to calculate the common velocity of pendulum and bullet after collision

m v = ( m + M ) V

m is mass of bullet M is mass of pendulum , v is velocity of bullet and V is their final velocity after collision.

V = m v / ( m + M )

= .030 x 185 / 3.18

= 1.745 m /s

The kinetic energy of bullet+pendulum  will be converted into potential energy.

1/2 (m+M) V² = ( m + M ) g h

h is height by which pendulum and bullet rises after collision

Putting the values

.5 x 3.18 x 1.745² = 3.18 x 9.8 x h

h = .155 m

If θ be the angle that the pendulum is making at deflected position

l - lcosθ = h , l is length of pendulum

2.85 ( 1 - cosθ) = .155

1 - cosθ = .054

cosθ = .946

θ = 19 degree

Horizontal displacement = 2.85 sin 19

= .9278 m

92.78 cm

for this one it would be d bump/forearm pass