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## Homework Statement

A projectile is thrown at angle θ with an inclined plane of inclination 45

^{o}.

Find θ if projectile strikes the inclined the plane horizontal

## Homework Equations

Taking x-axis along the incline and y-axis perpendicular to incline.[/B]

V

_{x}=ucosθ - gsint(45)t

V

_{y}=usinθ - gcos(45)t

These are the velocities after time t.

V

_{x}=Velocity along the plane after time t.

V

_{y}=Velocity perpendicular to plane after time t.

## The Attempt at a Solution

As at the time of horizontal collision with the incline. The projectile will make an angle of 45

^{o}with the incline and hence the velocity of projectile V=Vcos45

**i**+ Vsin45

**j**which means the x and y components of velocity are equal (as sin45=cos45).

And hence I applied the condition that V

_{x}=V

_{y}

that gives us:

ucosθ - gsint(45)t = usinθ - gcos(45)t

=> ucosθ-usinθ = gsin(45)t-gcos(45)t

=>u(cosθ-sinθ) = gt(sin45-cos45)

=>u(cosθ-sinθ)=0 (as sin45=cos45)

=>cosθ-sinθ=0

=>cosθ=sinθ => Tanθ=1

which gives θ=45

^{o}

But the answer is θ = tan

^{-1}(2) - 45

^{o}

I know how the right solution came but I am more bothered about what was wrong in my attempt that I got it incorrect.

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