A very thoughtful physics student takes her younger sibling to the arcade to play skeeball. She estimates the mass of the skee ball to be about 0.5 kg and the height of the fifty-point ring to be about 1 m above the position from which the ball is released.

a. How much gravitational potential energy will the ball have if it hits the fifty-point ring at the highest point?

b. How much kinetic energy does the ball need at its release to reach the highest point?

c. At what velocity must the ball be released to reach the highest point?

d. The student’s sibling uses a radar gun to determine how fast she releases the ball, and it is exactly the speed she calculated to reach the 1 m height. However, the ball lands in the thirty-point ring, which is 0.8 m above the release point. How much energy is lost to friction if the ball only reaches 0.8 m instead of 1 m?