Question

I need help answering this, I keep running into dead ends.

You are target shooting using a toy gun that fires a small ball at a speed of 15 m/s. When the gun is fired at an angle of 35 ∘ above horizontal, the ball hits the bull's-eye of a target at the same height as the gun. Then the target distance is halved.
At what angle must you aim the gun to hit the bull's-eye in its new position? (Mathematically there are two solutions to this problem; the physically reasonable answer is the smaller of the two.)

Answer 1

Use of the "range" formula will greatly simplify this -

R = V^2 sin 2 θ / g

R = 15^2 sin 70 / 9.8 = 21.6 m distance originally traveled

r = 21.6 /2 = 10.8 if distance is halved

sin 2 θ = 10.8 * 9.8 / 225 = 28.1 deg

θ = 14 deg