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!

Projectile from a cliff - ugh!

  1. Feb 13, 2010 #1
    1. The problem statement, all variables and given/known data
    A projectile fired up into the air from the top of a 75m high cliff hits the ground 500m out from the base.
    Calculate the initial launch velocity (U), and launch angle (theta) of the projectile.

    2. Relevant equations
    1) v=u+at
    2) v2=u2 +2as
    3) s=ut+0.5at2

    3. The attempt at a solution
    Consider up to be positive direction.
    Consider vertical component (y component) of motion for entire flight:
    a=-9.8 m/s2

    Sub into Eqn 3:
    -75=Usin(theta)t+0.5(-9.8)t2 #EQN A

    Consider horizontal component (x component) of motion for entire flight:

    Sub into Eqn 3:
    500=ucos(theta)t #EQN B

    Now comes the problem... I have created 2 equations (A,B), but with 3 unknowns (u, theta,t). I think I need another equation ???

    This is REALLY bugging me, please help.
    Thanks very much.
  2. jcsd
  3. Feb 13, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Your thinking is correct. You do need more information. The answer to this problem is not uniquely defined with the information that is given.
  4. Feb 13, 2010 #3
    OK thanks, but the book gives the answer as 65m/s at an angle of 40degrees to the horizontal.
    Could it be that I need to create another equation from my data ??

  5. Feb 13, 2010 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    As I said earlier, there are pairs of angles and initial speeds that give the same numbers. The numbers that are given by the problem do not uniquely define a solution. Try this:

    Assume that the angle is 40o and that the initial speed is 65 m/s.
    Solve your EQN B for the time of flight.
    Plug the numbers in the right side of EQN A; you should get -75 m.

    Now repeat but with an angle of 60o and initial speed 72.15 m/s and see what you get.

    The answer to this problem is not unique unless some other quantity is given to remove the ambiguity. You have created all the equations that can be created from what is given. To get another equation, you need more data.
  6. Feb 13, 2010 #5
    Thanks kuruman I see your point.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Projectile cliff Date
Projectile from cliff May 3, 2016
Projectile thrown horizontally off a cliff Oct 11, 2015
Projectile motion rock off a cliff Nov 23, 2013