7. 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)

c)

First of all we shall calculate the velocity of bullet just after the collision with the pendulum by applying conservation of momentum law.

v₂ = mv₁ / (m + M)

v₂ is velocity after the collision, m is mass of bullet v₁ is velocity of bullet and M is mass of pendulum.

v₂ =.030 x 185 / 3.18

= 1.745 m / s

Let the angle of the pendulum's maximum displacement with the vertical be θ

height attained by the pendulum h = L (1 - cosθ); L is the length of the string.

Applying conservation of mechanical energy law

mgh = 1/2 m v₂²

m is mass of (bullet + pendulum), v₂ is its velocity

g L (1 - cosθ) = v₂² / 2

9.8 x 2.85 (1 - cosθ) = 1.745² / 2

(1 - cosθ) =.0545

cosθ =.9455

θ = 19 degree

a) The vertical component of the pendulum's maximum displacement.

L (1 - cosθ)

= 2.85 (1 -.9455

=.155 m

b) Horizontal component : L sin18

= 3.15 x. 30

=.97 m.