# Projectiles On An Inclined Plane

1. Jul 30, 2013

### Woolyabyss

1. The problem statement, all variables and given/known data
A particle is projected with initial speed u at an angle tan-inverse(1/2) to an inclined plane. The plane contains the point of projection and makes an angle tan-inverse(3/4) with the horizontal. Show that the angle at which the particle strikes the plane is tan-inverse(2)

2. Relevant equations

the line of greatest slope of the inclined plane is the taken as the horizontal(i axis) and the perpendicular of the line of greatest slope is taken as the j axis.

S=ut + 1/2(a)(t^2)

V = u + at

3. The attempt at a solution

I tried to find the angle which the object was projected to the plane. I called it A

tan(( tan-inverse(1/2) - tan-inverse(3/4) ) = 2/11 ............ TanA =2/11

cosA = 11/(5√5) ...................... sinA = 2/(5√5)

I tried to find the time when the object lands This is when the perpendicular distance from the plane is zero( Sy = 0)

Sy = u(2u / 5√5)t - (1/2)(4g/5)t^2

simplify and t = u/(g√5)

the angle when the object lands is given by TanB = A | (Vy)/(Vx) | (where the time is when the object lands.)

Vy
= u(2u/5√5) - g(4/5)(u/g√5)

= 2u/5√5 - 4u/5√5

= -2u/5√5

Vx = u(11/5√5) - g(3/5)(u/g√5)

simplify and Vx = 8u/5√5

when you divide Vy/Vx = 1/4

Im not sure what I did wrong but I think it might be something to do with "The plane contains the point of projection".
Any help would be appreciated.

2. Jul 30, 2013

### ehild

You do not need to find that angle: it is given. Read the sentence in bold.

ehild

3. Jul 31, 2013

### Woolyabyss

Oh, For some reason I thought that it said it was the angle from the projection to the horizontal. I just did the question again using what you said and got the right answer. Thanks for the help.

4. Jul 31, 2013

### ehild

You are welcome. Nice solution!

ehild