(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A projectile is fired up an incline (incline angle φ) with an initial speed vi at an angle θi with respect to the horizontal (θi > φ). (a.) Show that the projectile travels a distance d up the incline, where

d = 2*vi^2*cosθi*sin(θi-φ) / g*cos(φ)^2

2. Relevant equations

[tex]v = v_0 + a t[/tex]

3. The attempt at a solution

I have tried 2 different approaches to this proof. The first strategy was to tilt the figure so that the distance d was parallel to the x axis. However, through some research I found that to rotate the problem, you will also need to find the components of gravity and things got hairy from there.

The second approach I took was to write the normal equations for x and y

( x= v_i cos (\theta_i) t, y= v_i sin ( \theta_i) t - 1/2 g t^2 ).

Then I plugged x= d cos (\phi) and y = d sin ( \phi) into the 2 above equations

I ended up with d(cos(phi)) = v_i(cos(θi))t

and d(sin(phi)) = v_i(sin(θi)t - .5gt^2

I was then told to isolate the t value from the first equation, and plug it into the second equation.

However, this resulted in a very complex equation and I was unable to solve it for d, which should have given me the initial equation I was trying to prove.

Am I making any errors, or should I try a different method?

Thanks

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

2. Relevant equations

3. The attempt at a solution

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

Join Physics Forums Today!

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

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

# Homework Help: Projectile Up Incline Proof

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