Question

a 100 kg student is compressed 50 cm on a spring with a spring constant of k = 80,000 N/m. He is on top of a 10 m frictionless hill. He then is released from rest. He goes down to the bottom of the hill before sliding up a 30° frictionless hill. a. (8 pts) Find the speed of the student when he reaches the bottom of the hill. b. (9 pts) Find the distance D the student travels up the hill before momentarily stopping. Use whichever method you wish.

Answer 1

The mass (m) of the student is 100kg, the spring has a spring constant (k) of 80000N/m, the compression of the spring (y) is 50cm, the height h of the hill is 10m, the initial velocity (u) of the student is zero since he is at rest and the inclinination of the other hill is 30degree.

Let initial position be position 1, bottom of the hill be position 2 and the final position at the top of the hill be position 3.

Applying the law of conservation of energy from the initial position to the bottom of the hill,

The speed of the student when he reaches the bottom of the hill is 19.90m/s.

Applying law of conservation of energy from the bottom of the hill to the top of the hill,

The student reached 20.20m up the hill. Now,

The distance D the student travels up the hill before momentarily stopping is 40.40m.