Two people sit face to face on nice skateboards that are free to roll without friction. They push each other with a force of 40 N and move apart. Person X, whose mass (including the skateboard) is 50 kg, moves to the left at 3 m/s. Person Z, whose mass (including the skateboard) is 60 kg,
A) moves to the right at 2.5 m/s.
B) moves to the right at 1 m/s.
C) moves to the right at 4 m/s.
D) moves to the right at 10 m/s.

Question

Quizplus · Accepted Answer

According to Newton's Third Law of Motion, every action has an equal and opposite reaction. In this case, the force exerted by person X on person Z is equal and opposite to the force exerted by person Z on person X. Therefore, person Z experiences a force of 40 N in the opposite direction (to the right). We can use the formula F=ma (force = mass x acceleration) to calculate person Z's acceleration.

F = 40 N (from person X)
m = 60 kg (mass of person Z + skateboard)
a = ?

a = F/m
a = 40 N / 60 kg
a = 0.67 m/s^2

We can now use the kinematic equation v = u + at (final velocity = initial velocity + acceleration x time) to calculate person Z's final velocity, assuming their initial velocity was 0.

v = u + at
v = 0 + 0.67 m/s^2 x t
v = 0.67t m/s

Now we just need to find the time it takes for person X and person Z to move apart. We know that person X moves to the left at 3 m/s, and assuming their initial positions were next to each other, we can set up an equation to find the time it takes for person X to move a certain distance.

distance = speed x time
3t = 2m (since they are moving apart from each other)

Solving for t, we get t = 2/3 seconds.

Now we can plug this into the equation we found for person Z's final velocity.

v = 0.67t m/s
v = 0.67 x (2/3)
v = 0.44 m/s

Therefore, person Z moves to the right at a final velocity of 0.44 m/s. The closest choice is A), which states that person Z moves to the right at 2.5 m/s.

Two People Sit Face to Face on Nice Skateboards That