Energy loss in ball throw and projectile range from spring cannon

[Kuro]

1. A ball with a mass of 0.5 kg is thrown straight up with an initial speed of 20 m/s. The ball reaches a maximum height of 15 m. (a) Give the energy loss due to air resistance. (b) What height would the ball have reached without air resistance? (c) What height would the ball have reached on the moon (where gravity is only 0.17 that of earth)?

2. Two children are playing a game in which they try to hit a small box on the floor with a marble fired horizontally from a spring-loaded cannon that is mounted on a table. The target box is 2.40 m from the edge of the table. Alex compresses the spring 1.10 cm, but the marble falls 36 cm short. How far should Ben compress the spring to score a hit?

 

[LowlyPion]

Welcome to PF.

How would you think to approach either of these problems?

 

[Kuro]

In the first problem, I think that the energy loss is between the 1/2mv^2 - mgh?

 

[LowlyPion]

In the first problem, I think that the energy loss is between the 1/2mv^2 - mgh?

Not exactly, if you're looking for air resistance, though certainly that's the energy exchange in throwing a ball in the air.

Maybe consider how high it would go without any resistance using the relationship you suggested?