A student with a mass of 40 kg can throw a 15-kg ball with a relative speed of 5.0 m/s.The student is standing at rest on a cart with a mass of 12 kg that can move over the ground without friction.If the student throws the ball horizontally,what is the speed of the ball relative to the ground?
A)1.4 m/s
B)3.1 m/s
C)3.9 m/s
D)5.0 m/s
E)5.9 m/s

Question

Quizplus · Accepted Answer

We can start by applying conservation of momentum in the horizontal direction. Initially, the momentum of the system is zero since both the student and the cart are at rest. After the ball is thrown, the momentum of the system is given by:

(m_student + m_cart + m_ball) * v = m_ball * v_ball

where v is the velocity of the student and cart after the throw and v_ball is the velocity of the ball relative to the ground.

Solving for v, we get:

v = (m_ball / (m_student + m_cart + m_ball)) * v_ball

Plugging in the given values, we get:

v = (15 kg / (40 kg + 12 kg + 15 kg)) * 5.0 m/s ≈ 3.9 m/s

Therefore, the speed of the ball relative to the ground is approximately 3.9 m/s. The correct answer is (C).

A Student with a Mass of 40 Kg Can Throw