Question

A toy gun uses a spring with a force constant of 350 N/m to propel a 15.0 g steel ball. The spring is compressed 8.40 cm and friction is negligible.

a) How much force (in N) is needed to compress the spring? (Assume the gun is aimed in the positive direction. Indicate the direction with the sign of your answer.)

b)To what maximum height (in m) can the ball be shot?

c)At what angles above the horizontal (in degrees) may a child aim to hit a target 3.00 m away at the same height as the gun? (Enter your answers to at least two decimal places.) smaller angle and larger angle?

* I already answered a and b: a) -29.4 N and b) 8.52 m, I just need C *

Answer 1

Let the velocity of bullet when it is fired = u

Mass of bullet = m = 15g =0.015 kg

Compression in spring = x = 8.4 cm = 0.084 m

Force constant of spring = k = 350 N/m

When the toy gun is fired, this potential energy gets converted into kinetic energy of bullet

   ….(1)

Child aims to hit a target 3 m away at the same height as the gun.

So, Range of projectile = 3 m

Formula for range of projectile is given by the formula

where u = initial velocity

θ = angle of projection

g = acceleration due to gravity

substituting values of range and u² in above formula, we get