A woman with a mass of 41 kg runs at a speed of 7 m/s and jumps onto a giant 30 kg skateboard initially at rest. What is the combined speed of the woman and the skateboard?
momentum is conserved
41 * 7 = v * (41 + 30)
To find the combined speed of the woman and the skateboard, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event.
The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) can be represented as:
p = m * v
Given that the woman has a mass of 41 kg and a speed of 7 m/s, her momentum can be calculated as:
woman's momentum = 41 kg * 7 m/s
Similarly, the momentum of the skateboard, which initially at rest (so its velocity is 0 m/s), can be calculated as:
skateboard's momentum = 30 kg * 0 m/s
Since the total momentum before the event is equal to the total momentum after the event, we have:
Total initial momentum = Total final momentum
After the woman jumps onto the skateboard, they move together as one system. Let's assume their combined speed is V. Then, the total final momentum can be calculated as:
Total final momentum = (mass of woman + mass of skateboard) * V
Using the conservation of momentum principle, we can equate the two expressions for total momentum:
41 kg * 7 m/s + 30 kg * 0 m/s = (41 kg + 30 kg) * V
Simplifying the equation, we get:
287 kg * m/s = 71 kg * V
To find the combined speed (V), we can rearrange the equation:
V = (287 kg * m/s) / (71 kg)
Evaluating the expression, we find:
V ≈ 4.05 m/s
Therefore, the combined speed of the woman and the skateboard after the jump is approximately 4.05 m/s.