1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Projectile Fired Up a Hill

  1. Aug 31, 2008 #1
    1. The problem statement, all variables and given/known data

    A projectile is fired with initial speed v0 at an elevation angle (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 range?

    2. Relevant equations

    x = v0tcos(alpha)
    y = -(gt^2)/2 + v0sin(alpha)
    r = (x^2 + y^2)^(1/2)

    3. The attempt at a solution

    I had thought that the solution to this problem might be as simple as finding where the line that represents the hill intersects with the line that represents the trajectory of the projectile. But I'm not sure how to get there from here. I would know how to solve this if the range I was concerned about was the range from where the projectile is launched to where it hits the ground again (i.e. y2 = 0), but this has me stumped. Anything to point me in the right direction would be appreciated!
  2. jcsd
  3. Aug 31, 2008 #2
    Hmm.. in the time I've had to think about this, I could only see one way to approach this, and it probably isn't the simplest approach.

    As you said, you need to find the intersection between the projectile path and the line that represent the hill. A projectile takes the path of a parabola, while the hill would be a linear line. Do you know how to find the cartesian equation of a parabolic projectile path? (hint: substitute the t's so you only have y and x).

    If you're stumped about the hill, just remember how to find the gradient of a line given its angle. Once you have TWO equations, it should just be a matter of algebra.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook