Concepts A toy gun uses a spring with a force constant of 300 N/m to propel a 10.0-g steel ball. If the spring is compressed 7.00 cm and friction is negligible: (a) How much force is needed to compress the spring? (b) To what maximum height can the ball be shot? (c) At what angles above the horizontal may a child aim to hit a target 3.00 m away at the same height as the gun? (d) What is the gun’s maximum range on level ground?

Step-by-step solution Step 1 of 7 Power is the rate at which work is done, or in equation form, for the average power P for work W done over a time t. The SI unit for power is the watt (W) here 1 watt equals 1 joule/second. Step 2 of 7 (a). Calculate the magnitude of the force by the formula which is needed to compress the spring: Substitute for k and for , Hence, the magnitude of the force is . Step 3 of 7 (b). The maximum height the ball can be reached, is calculated as follows, Rearrange the equation in terms of , Substitute for k, for , for m and for , Hence, the maximum height the ball can be reached is . Step 4 of 7 (c). The angle above the horizontal that a child may aim to hit the target away at the same height as the gun is calculated by following formula, Rewrite the above formula for , Substitute for ,