Maximizing Projectile Range on a Sloped Ramp

[dan_and_sim]

Homework Statement

A toy cannon is placed on a ramp that has a slope of angle alpha = Pi/8. The
cannonball is projected up the hill at an angle of pheta above the horizontal (see
figure) and has a muzzle speed of v0 = 4.2 m s−1.

(a) Given pheta = Pi/5, compute R, the range of the cannonball, as measured
along the ramp.
(b) What angle  do you have to choose to ensure that the cannonball flies
horizontally when hitting the ramp?
(c) What angle  do you have to choose to obtain maximal range R?

Homework Equations

The Attempt at a Solution

The only way i can think to calculate this is by considering the slope of the hill to be the ground level and then correcting gravity by splitting it into gcos(pi/8) and gsin(pi/8)

would this approach yield the correct results?

 

[jbsteele]

a) R=v0^2/g sin(2pheta)/cos(pi/8)b) pheta = pi/2 - pi/8c) pheta = arcsin[ gcos(pi/8) / (2gsin(pi/8))]