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 motion trajectories differing from 45 degrees

  1. Apr 13, 2015 #1
    Hi guys, I am stuck with a problem here.
    First, It is given that for 2-dimensional projectile motion, a trajectory of 45 degrees will yield the greatest range. However, how do I show that angles that differ from 45 degrees by the same amount will yield the same range? For example, the range of a 40 degree angle will equal that of a 50 degree angle?

    I know that the range of a projectile as a function of time is given by V^2 * sin(2ø) / g where V is the initial velocity and ø is the angle. I just don't know how to prove that the angle 45 + c will give give the same range as 45 - c, can anyone help me please?
  2. jcsd
  3. Apr 13, 2015 #2
  4. Apr 13, 2015 #3
    Oh I see,
    since sin(α + β) = sin(α)cos(β) + cos(α)sin(β),
    and cos(90) = 0, I am left with sin(a)cos(B) in both cases,
    thanks for the help!
  5. Apr 14, 2015 #4
    It is cos (c) in both cases. Sin of 90 is 1 and cos (-c)=cos (c).
  6. Apr 18, 2015 #5
    But how this answers @bongobl's question?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Projectile motion trajectories Date
B Need help with projectile motion problem Nov 2, 2017
B Equation For Trajectory May 17, 2017
B Finding length of an arc produced by projectile Feb 15, 2017
To Study Trajectory Of Shuttlecock In Badminton Feb 4, 2015