A 500-kg roller coaster car travels with some initial velocity along a track that is 5 m above the ground. The car goes down a small hill and then coasts back up a higher hill. The second hill is 12 m above the ground. What must the initial velocity of the car be for the car to be going 3 m/s at the top of the second hill?

Aspring has a relaxed length of 33 cm (0.33 m) and its spring stiffness is 6 n/m. you glue a 76 gram block (0.076 kg) to the top of the spring, and push the block down, compressing the spring so its total length is 15 cm. you make sure the block is at rest, then at time t=0 you quickly move your hand away. the block begins to move upward, because the upward force on the block by the spring is greater than the downward force on the block by the earth. calculate y vs. time for the block during a 0.09-second interval after you release the block, by applying the momentum principle in three steps each of 0.03-second duration.