A 29-g rifle bullet traveling 240 m/s embeds itself in a 3.0kg pendulum hanging

Question

A 29-g rifle bullet traveling 240 m/s embeds itself in a 3.0kg pendulum hanging on a 2.5m-long string which makes the pendulum swing upward in an arc. Determine the vertical component of the pendulum's maximum displacement Express your answer to two significant figures and include the appropriate units. ANSWER Delta y_max = __________ Determine the horizontal component of the pendulum's maximum displacement. Express your answer to two significant figures and include the appropriate units. ANSWER delta x_max = ______________

Explanation / Answer

Let v = velocity of the pendulum with embedded bullet immediately after the impact

By the law of conservation of linear momentum,

0.029 * 240 + 0 = (0.029 + 2.5) v

6.96 = 2.529v

v = 2.752 m/s

Let h = maximum height of the pendulum in its swing

By the law of conservation of kinetic energy after the impact,

(1/2) mv^2 = mgh

h = v^2/2g

h = (2.752)^2 / (2 * 9.81) = 0.3864 m

vertical displacement = 0.3864 m upwards

and horizontal displacement

= [2.5^2 - (2.5 - 0.3864)^2]

= [6.25 - 4.4673]

= 1.335 m.

Answer:

Vertical displacement = 0.3864 m

Horizontal displacement = 1.335 m

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