# Do I use a system of equations for this projectile motion?

#### phantomcow2

1. Chuck Norris kicks a basketball from the ground into a basketball hoop, it makes it in perfectly. THe hoop is 150m away, and 6m above the ground. He kicks the ball at a 39 degree angle. How long does it take for the ball to reach the net? What was the initial velocity?

2. X1=X0+v0t+1/2at^2

3. So breaking it down, I know that Vox = v0cos(39)
And that voy= v0Sin(39

Doesn't that mean I use the tangent function? Can somebody jumpstart my memory? #### phantomcow2

A little background:
As a homework assignment, we were told to make up a moderate problem and share with the class as a review for upcoming midterms. I solved one of these a few months ago and cannot remember at all how.

#### cristo

Staff Emeritus
Your components of velocity are correct. Try writing your equation out twice; once for vertical and once for horizontal motion.

#### Doc Al

Mentor
2. X1=X0+v0t+1/2at^2
That's a good generic equation. Hint: Write separate equations for the horizontal and vertical motions. (How do they differ?)

3. So breaking it down, I know that Vox = v0cos(39)
And that voy= v0Sin(39

This is good. Combine this with the above equations and you'll be able to solve for V0.

H

#### Haywire

##### Guest
Once you write the equation for the horizontal motion, try to solve it to get $v_0t$ and substitute it in the equation for verticle motion. This will give you time! Try it!

#### phantomcow2

So
150=0+v0Sin(39) + 1/2*0*t^2
6=0+v0Cos(39) + 1/2*-9.81t^2

From here, doesn't tangent end up replacing Sin and Cosine though?

#### Doc Al

Mentor
So
150=0+v0Sin(39) + 1/2*0*t^2
6=0+v0Cos(39) + 1/2*-9.81t^2
You've mixed up your sines and cosines.

From here, doesn't tangent end up replacing Sin and Cosine though?
No. You know the sine and cosine, so they are just numbers. Combine the two equations and solve for v0.

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