Questions: A woman with a mass of 60 kg runs at a speed of 6 m/s and jumps onto a giant skateboard with a mass of 40 kg. What is the combined speed of the woman and the skateboard?

A woman with a mass of 60 kg runs at a speed of 6 m/s and jumps onto a giant skateboard with a mass of 40 kg. What is the combined speed of the woman and the skateboard?

Transcript text: Question 24 3 pts A woman with a mass of 60 kg runs at a speed of $6 \mathrm{~m} /$ and jumps onto a giant skateboard with a mass of 40 kg . What is the combined speed of the woman and the skateboard?

Solution

Solution Steps

Step 1: Identify the Conservation Principle

The problem involves a collision where the woman jumps onto the skateboard. We use the principle of conservation of momentum, which states that the total momentum before the collision equals the total momentum after the collision.

Step 2: Calculate Initial Momentum

The initial momentum is the momentum of the woman since the skateboard is initially at rest. The formula for momentum is:

\[ p = mv \]

where $ m $ is mass and $ v $ is velocity.

For the woman: \[ p_{\text{woman}} = 60 \, \text{kg} \times 6 \, \text{m/s} = 360 \, \text{kg} \cdot \text{m/s} \]

Step 3: Set Up the Equation for Final Momentum

The final momentum is the combined momentum of the woman and the skateboard moving together at a common velocity $ v_f $.

\[ p_{\text{final}} = (m_{\text{woman}} + m_{\text{skateboard}}) \times v_f \]

Substitute the known values: \[ 360 \, \text{kg} \cdot \text{m/s} = (60 \, \text{kg} + 40 \, \text{kg}) \times v_f \]

Step 4: Solve for the Final Velocity

Solve the equation for $ v_f $:

\[ 360 = 100 \times v_f \]