# Trig question I think

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• Sep 7th 2008, 03:37 AM
BrainZero
Trig question - URGENT!!! Desperately need help!
DESPERATELY IN NEED OF HELP!!!

If a projectile is fired from the origin(of the xy-plane) with an initial velocity v at an angle of theta above the horizontal, then its trajectory(ignoring air resistance) is the parabola

y = tan(theta) x - [g/(2v^2(cos(theta)^2)] * x^2 where 0<theta<Pi/2

where g is the gravitational constant.

Suppose the projectile is fired from the base of a plane that is inclined at a constant angle alpha,(alpha >0), upwards from the horizontal, and lands on this plane at the point P. The range R is the distance from the origin to P and clearly depends upon the initial angle theta. Show that

R(theta) = 2v^2/(g(cos alpha)^2) * cos(theta)sin(theta-alpha)

I have no clue as to how to start even. I really don't understand the problem. Could somebody draw up a diagram for me so that I can better understand the problem? I am not sure how alpha and theta are related. I don't know if I am having trouble understanding the English or the math. It's probably both! (Thinking)
• Sep 7th 2008, 04:45 AM
mr fantastic
Quote:

Originally Posted by BrainZero
If a projectile is fired from the origin(of the xy-plane) with an initial velocity v at an angle of theta above the horizontal, then its trajectory(ignoring air resistance) is the parabola

y = tan(theta) x - [g/(2v^2(cos(theta)^2)] * x^2 where 0<theta<Pi/2

where g is the gravitational constant.

Suppose the projectile is fired from the base of a plane that is inclined at a constant angle alpha,(alpha >0), upwards from the horizontal, and lands on this plane at the point P. The range R is the distance from the origin to P and clearly depends upon the initial angle theta. Show that

R(theta) = 2v^2/(g(cos alpha)^2) * cos(theta)sin(theta-alpha)

I have no clue as to how to start even. I really don't understand the problem. Could somebody draw up a diagram for me so that I can better understand the problem? I am not sure how alpha and theta are related. I don't know if I am having trouble understanding the English or the math. It's probably both! (Thinking)

It's your lucky day - Read the attachment.
• Sep 7th 2008, 05:13 AM
BrainZero
That was a lot of algebra. Thanks. (Speechless)