Solving for initial velocity Projectile Motion

AI Thread Summary
A rock is thrown from a 20-meter high building at a 53-degree angle, with its horizontal range equal to the building's height. The equations of motion are applied to find the initial speed and time of flight. The user attempts to solve for time using the horizontal motion equation but struggles with the vertical motion equation. They recognize a potential mistake in the sign of the displacement due to gravity. The discussion focuses on correctly applying the equations to determine the rock's initial velocity and time in the air.
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Homework Statement


A rock is thrown from the top of a twenty meter high building at the angle 53 degrees above the horizontal. IF the horizontal range of the throw is equal to the height of the building, what is the speed of the rock? How long is it in the air? What's the velocity of the rock before it hits the ground?



Homework Equations


Vx = Vox
Vy = Voy - gt
x = xo + Voxt
y = yo + Voy - (1/2)gt^2


The Attempt at a Solution


I use the second one and set x = to 20 and solve for the time...

20 = 0 + Vcos(53)t
t = 20/Vcos(53)

I substitute into the y equation

20 = vsin(53) - 1/2g(20/vcos(53)^2

Here is where I think I'm making the big mistake... help! :(
 
Physics news on Phys.org
The displacement y is along g. So it must be -ve
So rewrite the equation and solve for v.
 

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