A 42.5 kg student runs down the sidewalk and

jumps with a horizontal speed of 4.16 m/s
onto a stationary skateboard. The student
and skateboard move down the sidewalk with
a speed of 3.97 m/s.
a) Find the mass of the skateboard.

To find the mass of the skateboard, we can use the principle of conservation of momentum. According to this principle, the total momentum before and after the jump should be the same.

Before the jump, we have a student with a mass of 42.5 kg and a horizontal speed of 4.16 m/s. Since the skateboard is stationary, its momentum is zero.

After the jump, the student and the skateboard move together with a speed of 3.97 m/s. Let's assume the mass of the skateboard is m kg.

Using the conservation of momentum, we can write the equation:

(mass of student) × (initial speed of student) = (mass of skateboard + mass of student) × (final speed of both student and skateboard)

Plugging in the given values:

(42.5 kg) × (4.16 m/s) = (m kg + 42.5 kg) × (3.97 m/s)

Now, we can solve this equation to find the mass of the skateboard.

42.5 kg × 4.16 m/s = (m + 42.5 kg) × 3.97 m/s

176.8 kg·m/s = (m + 42.5 kg) × 3.97 m/s

Dividing both sides of the equation by 3.97 m/s:

176.8 kg·m/s / 3.97 m/s = m + 42.5 kg

44.5 kg = m + 42.5 kg

Subtracting 42.5 kg from both sides of the equation:

44.5 kg - 42.5 kg = m

2 kg = m

Therefore, the mass of the skateboard is 2 kg.

Now Angel, this is very similar to the one I answered for you.

Momentum after = momentum before.