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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 xaxis along the incline and yaxis 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=Vcos45i + Vsin45j 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
=> ucosθusinθ = gsin(45)tgcos(45)t
=>u(cosθsinθ) = gt(sin45cos45)
=>u(cosθsinθ)=0 (as sin45=cos45)
=>cosθsinθ=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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