the following problem is from the 5th edition of Thorton and Marion's "Classical Dynamics"(adsbygoogle = window.adsbygoogle || []).push({});

ch.2 problem 14 p.92

The problem statement, all variables and given/known data

A projectile is fired with initial speed v_0 at an elevation angle of alpha up a hill of slope beta (alpha > beta).

(a) how far up the hill will the projectile land?

(b) at what angle alpha will the range be a maximum?

(c) what is the maximum angle?

The attempt at a solution

apparently this has been a stumper in former classical mechanics classes, but here was as far as i got:

i broke down the components of the forces into x and y

x-component:

a_x=0 integrating -->

v_x = v_0 cos(beta) integrating -->

x = v_0 t cos(beta)

a_y = -g integrating -->

v_y = -gt + v_0 sin (alpha - beta) integrating -->

y = ( -gt^2 / 2 ) + v_0 sin (alpha - beta)

the answer in the back of the book for part (a) is:

d = (2 v_0^2 cos(alpha) sin(alpha-beta) ) / (g cos^2(beta))

any idea how to get from the components to the answer?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Projectile Fired Up A Hill

**Physics Forums | Science Articles, Homework Help, Discussion**