A 2.0-kg object moving 3.0 m/s strikes a 1.0-kg object initially at rest.Immediately after the collision,the 2.0-kg object has a velocity of 1.5 m/s directed 30$\degree$ from its initial direction of motion.What is the x component of the velocity of the 1.0-kg object just after the collision?
A)3.7 m/s
B)3.4 m/s
C)1.5 m/s
D)2.4 m/s
E)4.1 m/s

Question

Quizplus · Accepted Answer

We can use conservation of momentum in the x direction to solve for the velocity of the 1.0-kg object:
(m1)(v1) + (m2)(v2) = (m1 + m2)(vf)
where m1 = 2.0 kg, v1 = 3.0 m/s, m2 = 1.0 kg, v2 = 0 m/s, vf is the final velocity of both objects. We can then solve for vf:
(2.0 kg)(3.0 m/s) + (1.0 kg)(0 m/s) = (2.0 kg + 1.0 kg)(vf)
6.0 kg-m/s = 3.0 kg(vf)
vf = 2.0 m/s
Now we can use trigonometry to solve for the x component of the velocity of the 2.0-kg object:
v2x = v2cosθ = (1.5 m/s)(cos30°) = 1.3 m/s
Since momentum is conserved, the x component of the velocity of the 1.0-kg object must be:
v1x = (m1v1x + m2v2x)/(m1 + m2) = (2.0 kg)(3.0 m/s - 1.3 m/s)/(2.0 kg + 1.0 kg) = 0.7 m/s
Therefore, the answer is B) 3.4 m/s.

A 20-Kg Object Moving 3 °\degree° From Its Initial Direction of Motion

A 20-Kg Object Moving 3 $\degree$ From Its Initial Direction of Motion