A person is standing on and facing the front of a stationary skateboard while holding a construction brick. The mass of the person is 87.0 kg, the mass of the skateboard is 4.10 kg, and the mass of the brick is 2.50 kg. If the person throws the brick forward (in the direction they are facing) with a speed of 15.0 m/s relative to the skateboard and we ignore friction, determine the recoil speed of the person and the skateboard.
My incorrect work:
p=mv
(Brick) p = 2.5 * 15
p = 37.5
Person and Board:
P = mv
37.5 = 91.1 * v
v = 0.4116
The website marks this incorrect. Help?
To solve the problem correctly and find the recoil speed of the person and the skateboard, we can apply the law of conservation of momentum. According to this principle, the total momentum before an event must equal the total momentum after the event, assuming no external forces are acting.
Let's define our coordinate system, where any movement in the forward direction is positive, and any movement in the backward direction is negative.
Given information:
Mass of person (m1) = 87.0 kg
Mass of skateboard (m2) = 4.10 kg
Mass of brick (m3) = 2.50 kg
Velocity of brick relative to skateboard (v3) = 15.0 m/s
Before the person throws the brick, both the person and the skateboard are stationary. Therefore, their initial velocities (v1i and v2i) are zero.
Now, let's apply conservation of momentum and write an equation for the system:
Total momentum before = Total momentum after
(m1 * v1i) + (m2 * v2i) = (m1 * v1f) + (m2 * v2f)
Since both the person and the skateboard move together after the throw, their final velocities (v1f and v2f) are the same. Let's call it vf.
Substituting the given masses and velocities:
(87.0 kg * 0) + (4.10 kg * 0) = (87.0 kg * vf) + (4.10 kg * vf)
0 = 91.1 kg * vf + 4.10 kg * vf
Combining like terms:
0 = 95.2 kg * vf
Since the sum of the initial momenta is zero, the final momentum must also be zero. This implies that the recoil speed (vf) of both the person and the skateboard is zero. Therefore, they remain stationary after the brick is thrown.
So, the correct answer is that the recoil speed of the person and the skateboard is 0 m/s.