# Projectile motion Problem :/

1. Sep 18, 2010

### physics_noob2

1. The problem statement, all variables and given/known data

Physics question: A golfball with an initial speed of 57.9 m/s lands exactly 85 m downrange on a level course. The acceleration of gravity is 9.8 m/s^2
Neglecting air friction, what minimum projection would achieve this result ? What maximum projection would achieve this result ? Answer in units of degrees Please.

2. Relevant equations

3. The attempt at a solution

Viy=57.9 sin theta
ay= -9.8
delta y=0

vix=57.9 cos theta
ax= 0
delta x=85

from horizontal,
t= 85/(57.9 cos theta)
from vertical,
0 = (57.9 sin theta) t + 1/2 (-9.8) (t)^2

So i tried doing it and got to the point so far and got stuck (can't seem to do the algebra). can anyone show me how to do this please Thanks.

2. Sep 19, 2010

### Delphi51

Sub the expression you have for t into the vertical equation. Get all your trig functions together on the left and the numbers on the right. You'll have sin(θ)*cos(θ) = a number.
Use the trig identity that sin(θ)*cos(θ) = ½*sin(2θ)
and you'll quickly get one value for 2θ. The other angle that gives the same sine is 180 degrees minus the first value (check it out on a unit circle sketch). Divide by 2 to get the two values for θ.

It is just a little easier if you use V = Vi + at for the vertical part instead of the distance formula. I always begin by writing both because you never know in advance which will be easier to work with.