- #1

Kavorka

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A toy cannon is placed on a ramp on a hill, pointing up the hill. With respect to the x-axis the hill has a slope of angle A and the ramp has a slope of angle B. If the cannonball has a muzzle speed of v, show that the range R of the cannonball (as measured up the hill, not along the x-axis) is given by:

R = [2v^2 (cos^2 (B))(tan(B) - tan(A))] / [g cos(A)]

The base equation we've derived for projectile range on a flat surface:

R = (v^2 /g)sin(2θ)

from the parabolic equation:

y = vt + (1/2)at^2 (where v is initial velocity, and v and a are in the y-direction)

and setting y to 0.

I'm not completely sure how to correctly start this problem or how to properly take the angle of the slope of the hill into account, the trig is a bit overwhelming. Even a good shove in the right direction would help immensely!