It's been a great day of new, frictionless snow. Julie starts at the top of the 60° slope with a push-off velocity of 1.7 m/s as shown in the diagram. At the bottom a circular arc carries her through a 90° turn, and then she launches off a 3.0-m-high ramp. How far horizontally is her touchdown point (in m) from the end of the ramp assuming that air resistance is negligible and that the local acceleration due to gravity is 9.80 m/s2?

You built a pinball machine that has a banked circular track with radius 0.34 m. The ball shooter launches the ball directly into this circular track before the ball enters into the game. You fire pin balls at a constant speed into the track and adjust the banking angle until it works. The banking angle is 21 degrees. Assume your pin ball machine is on a horizontal plane, how fast is the ball launched into the track, in m/s? Hint: I have a video on this problem about swing pendulum but the results are very similar, except a string length was given instead of path radius and tension was present instead of normal force. Assume friction is negligible.

6. A crazy, young boy on a sled is able to get up to an incredible speed of 22.5 m/s (yes, he is wearing a helmet!) along a frictionless horizontal surface while he approaches an icy hill with a vertical height of 11 m, as shown. He makes it to the top, and then flies off horizontally from the ledge of the hill. How far from the base of the hill does the boy land? 225 mis Figure 1

A ball is suspended from a light 1.3 m string . The string makes an angle of 24 degrees with the vertical. The ball is then kicked up and to the right such that the string remains taut the entire time the ball swings upwards. This kick gives the ball an initial velocity of 1.1m/s. What will be the speed, in meters per second, of the ball when it reaches its lowest point (θ = 0)?  What will be the maximum angle, in degrees, the string will make with the vertical?