A super dart of mass 20 g,traveling at 350 m/s,strikes a steel plate at an angle of 30° with the plane of the plate,as shown in the figure.It bounces off the plate at the same angle but at a speed of 320 m/s.What is the magnitude of the impulse that the plate exerts on the bullet?
A)0.52 N ∙ s
B)4.3 N ∙ s
C)300 N ∙ s
D)6.7 N ∙ s
E)0.30 N ∙ s

Question

A super dart of mass 20 g,traveling at 350 m/s,strikes a steel plate at an angle of 30° with the plane of the plate,as shown in the figure.It bounces off the plate at the same angle but at a speed of 320 m/s.What is the magnitude of the impulse that the plate exerts on the bullet? 
A)0.52 N ∙ s 
B)4.3 N ∙ s 
C)300 N ∙ s 
D)6.7 N ∙ s 
E)0.30 N ∙ s

Quizplus · Accepted Answer

We can use the impulse-momentum theorem which states that the impulse imparted on an object is equal to the change in momentum of the object.

Let's first find the initial momentum of the dart:

p1 = m1v1 = (0.02 kg)(350 m/s) = 7 kg m/s

The dart bounces off the plate, so its change in velocity is:

Δv = v2 - v1 = 320 m/s - 350 m/s = -30 m/s

The negative sign indicates that the dart is rebounding in the opposite direction.

The final speed of the dart is not needed to solve the problem, we only need the change in momentum:

Δp = m1Δv = (0.02 kg)(-30 m/s) = -0.6 kg m/s

By the principle of conservation of momentum, the impulse imparted on the dart by the plate is equal in magnitude but opposite in direction:

|J| = |Δp| = 0.6 N ∙ s

Therefore, the correct choice is D) 6.7 N ∙ s.

A Super Dart of Mass 20 G,traveling at 350 M/s,strikes