A friend is making an iMovie and wants your help designing a skateboard stunt. You estimate that your friend�s mass is four times greater than that of the skateboard. For the following questions, ignore friction.
In one scenario, your friend starts by standing at rest on the skateboard, and then jumps horizontally off of the skateboard. In order for the skateboard to shoot out with a speed of 10 meters per second, how fast should your friend jump (relative to the ground)?
A. none of these
B. 2.5 meters per second
C. 2 meters per second
D. 25 meters per second
E. 10 meters per second
To solve this problem, we can use the principle of conservation of linear momentum. According to the principle, the total momentum before the friend jumps off the skateboard should be equal to the total momentum after the friend jumps off.
Let's denote the mass of the friend as M and the mass of the skateboard as m. Given that the friend's mass is four times greater than that of the skateboard, we have M = 4m.
Let's assume the initial velocity of the skateboard is V_s and the initial velocity of the friend is V_f. After the friend jumps off, the skateboard shoots out with a speed of 10 meters per second. We need to find the velocity of the friend's jump, V_f.
Before the jump, the total momentum is given by (M + m) * 0, since both the friend and the skateboard are at rest initially.
After the jump, the total momentum is given by (M * V_f) + (m * V_s), where V_s is the velocity of the skateboard after the friend jumps off.
According to the conservation of linear momentum, these two momenta should be equal. Therefore, we have:
(M + m) * 0 = (M * V_f) + (m * V_s)
Since the skateboard shoots out with a speed of 10 meters per second, we have V_s = 10 m/s. Plugging in M = 4m and solving for V_f, we get:
(4m + m) * 0 = (4m * V_f) + (m * 10)
Simplifying the equation, we have:
5m * 0 = 14m * V_f
0 = 14m * V_f
From this equation, we can see that V_f must be 0 in order for both sides to equal zero. Therefore, the answer is none of these (option A).
So, in order for the skateboard to shoot out with a speed of 10 meters per second, the friend should jump off with a velocity of 0 relative to the ground.