Projectile motion

1. Apr 25, 2013

|mathematix|

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

A particle is projected at 30 m/s from the foot of a plane which is inclined at 30o to the horizontal. The particle hits the plane at an angle perpendicular to the plane.
Find the value of the angle of projection θ and the time taken to reach there.

2. Relevant equations

x=30tcosθ , and y=30tsinθ-5t^2 , where (x,y) are the coordinates of the point of impact and θ is the angle of projection, inclined with the horizontal.

3. The attempt at a solution

Here is a diagram: http://i.imgur.com/FfTwTD7.png
So if the projected particle hits the hill at 90o then y/x=1/√3 and the velocity will be at 120o to the horizontal so y'/x'=-√3
I solved these two equations simultaneously and I got θ=-60 but this looks wrong because it doesn't make sense.
Please help :)

Last edited: Apr 25, 2013
2. Apr 25, 2013

tiny-tim

hi |mathematix|!
shouldn't |y'| be larger than |x'| ?

3. Apr 25, 2013

|mathematix|

Yes, I fixed it :(

4. Apr 25, 2013

tiny-tim

is your answer ok now?

if not, show us your full working, so we can see what went wrong

5. Apr 25, 2013

|mathematix|

I did the working using the correct values but I got -60 degree for theta. I can't post the full solution now because it would take time and I have to study english now so I will re do it and see if I get a better answer.
I basically substituted the equations of motion into y/x=1/√3 and y'/x'=-√3 and then solved them simultaneously, found theta and substituted back to find the time, is that the correct approach?

6. Apr 25, 2013

tiny-tim

yes!

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