Question

a spring-loaded gun can fire a projectile to a height h if it is fired straight up. if the same gun is pointed at an angle of 45° from the vertical, what maximum height can now be reached by the projectile?

Answer 1

1/2 m v^2 = m g H by conservation of energy for an object fired straight up or

H = v^2 / (2 * g)

For an object traveling at 45 deg then

Vy = V sin 45 = 2^1/2 / 2 * V

So now

H = 1/2 * v^2 / (2 * g) = v^2 / (4 * g)

and the projectile will travel H / 2 instead of H