# Problem: A child's toy consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. The spring has a spring constant K, the ball has a mass M, and the ramp rises a height Y above the table, the surface of which is a height H above the floor.Initially, the spring rests at its equilibrium length. The spring then is compressed a distance S, where the ball is held at rest. The ball is then released, launching it up the ramp. When the ball leaves the launching ramp its velocity vector makes an angle THETA with respect to the horizontal.Throughout this problem, ignore friction and air resistance.1) Calculate Vr, the speed of the ball when it leaves the launching ramp.Express the speed of the ball in terms of K, S, M, Y, G, and/or .H2) With what speed will the ball hit the floor, Vf?Express the speed in terms of K, S, M, Y, G, and/or .H

###### FREE Expert Solution

Conservation of energy:

$\overline{){\mathbf{P}}{{\mathbf{E}}}_{{\mathbf{i}}}{\mathbf{+}}{\mathbf{K}}{{\mathbf{E}}}_{{\mathbf{i}}}{\mathbf{=}}{\mathbf{P}}{{\mathbf{E}}}_{{\mathbf{f}}}{\mathbf{+}}{\mathbf{K}}{{\mathbf{E}}}_{{\mathbf{f}}}}$

1)

PE = mgH and KE = 1/2mv2 ###### Problem Details

A child's toy consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. The spring has a spring constant K, the ball has a mass M, and the ramp rises a height Y above the table, the surface of which is a height H above the floor.

Initially, the spring rests at its equilibrium length. The spring then is compressed a distance S, where the ball is held at rest. The ball is then released, launching it up the ramp. When the ball leaves the launching ramp its velocity vector makes an angle THETA with respect to the horizontal.

Throughout this problem, ignore friction and air resistance.

1) Calculate Vr, the speed of the ball when it leaves the launching ramp.

Express the speed of the ball in terms of K, S, M, Y, G, and/or .H

2) With what speed will the ball hit the floor, Vf?

Express the speed in terms of K, S, M, Y, G, and/or .H