A woman with a mass of 50kg runs at a speed of 8m/s and jumps onto a giant skateboard with a mass of 25kg. What is the combined speed of the woman and the skateboard?
conserve momentum.
50*8 + 25*0 = (50+25)*v
I think it is 600. Anonymous, do me a favor and go to my question and answer it. k?
Come on. You're saying that when the woman jumps on the skateboard, she speeds up from 8m/s to 600m/s ??
Do a sanity check when you think you have an answer.
The next step is
400 = 75v
Still think v=600?
ok, fine...
So what’s the answer??
To calculate 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 the woman jumps onto the skateboard should be equal to the total momentum after she jumps.
Momentum (p) is the product of an object's mass (m) and its velocity (v):
p = m * v
Before the woman jumps, her momentum can be calculated as:
p_woman = m_woman * v_woman
Given that the woman's mass is 50 kg and her velocity is 8 m/s, we can substitute these values into the equation:
p_woman = 50 kg * 8 m/s = 400 kg·m/s
Similarly, the initial momentum of the skateboard can be calculated as:
p_skateboard = m_skateboard * v_skateboard
Given that the skateboard's mass is 25 kg and its velocity is initially zero (as it is not moving), we can substitute these values into the equation:
p_skateboard = 25 kg * 0 m/s = 0 kg·m/s
Since the skateboard is initially at rest, its momentum is zero.
According to the principle of conservation of momentum, the total momentum before the woman jumps is equal to the total momentum after she jumps. Therefore:
p_total_before_jump = p_woman + p_skateboard = p_total_after_jump
The woman's final momentum after the jump can be calculated using the combined mass of the woman and the skateboard (m_combined) and their combined velocity (v_combined):
p_combined = m_combined * v_combined
Given that the combined mass is the sum of the woman's mass (50 kg) and the skateboard's mass (25 kg):
m_combined = 50 kg + 25 kg = 75 kg
Substituting the combined mass into the equation, we get:
p_combined = 75 kg * v_combined
Since the total momentum before and after the jump stays the same:
p_woman + p_skateboard = p_combined
400 kg·m/s + 0 kg·m/s = 75 kg * v_combined
Simplifying the equation, we have:
400 kg·m/s = 75 kg * v_combined
Now, we can calculate the combined velocity (v_combined) by rearranging the equation:
v_combined = (400 kg·m/s) / 75 kg
v_combined ≈ 5.33 m/s
Therefore, the combined speed of the woman and the skateboard after she jumps onto it is approximately 5.33 m/s.