# Initial Velocity of a projectile, how?

1. Sep 13, 2009

### free-node-5

Initial Velocity of a projectile, how???

If I have a problem that says the x and y distance of a target from a starting position, and only gives the angle at which the particle is launched, how do I find the required initial Velocity for its launch?

I've been given the following equations to work with:
Vf = Vi + at
xf = xi + Vit + (.5)at2

I've spent hours trying to find a solution like this and can't seem to get anywhere. At one point I wrote out a huge equation with a bunch of trig stuff and it said a human threw a ball at over 513m/s so I know it must have been wrong.
One line I have written in my work says:
1.05=( Visin43 )/( Vicos43 ) - ( 4.9 * 9 )/( Vi cos 43 )
but I'm just asking in general, how do you do this???

2. Sep 13, 2009

### kuruman

Re: Initial Velocity of a projectile, how???

If you are given the x and y distance, in general, you use the first equation to solve for t in terms of x then plug that in the second equation, That gives you y as a function of x with the initial speed and angle as parameters. Use the third equation to find the maximum height reached by the projectile, in general.

3. Sep 13, 2009

### free-node-5

Re: Initial Velocity of a projectile, how???

I took what you said to heart and I still seem to just be making a mess.

Here are a few lines from my work:
1.05 = Vy(xf/Yix) - 4.9 ( xf2 / Vix2 )
...
1.05 = 9 tan43 - 4.9 ( 80 / Vix2 )
...
Vix = .136 ???
...
t = xf / Vix
t = 9 / .136 = 66.176

seems like a long time for something to get to a target that close :-/

Do you think you could show me or maybe just give an example?
My values are $$\theta$$=43(degrees), xi = 0, yi = 0, xf = 9, yf = 1.05

thanks

4. Sep 13, 2009

### kuruman

Re: Initial Velocity of a projectile, how???

Can you state the problem exactly the way it is given? Your interpretation of the given quantities may be in error.

5. Sep 13, 2009

### free-node-5

Re: Initial Velocity of a projectile, how???

quoting is probably not a good idea but trust me they were pretty straight-forward
There was even a diagram below the problem

--
A guy who's 2 meters tall, stands 9 meters horizontally from a ball-hoop mounted 3.05m high.
He throws the ball at an angle of 43 degrees from the horizontal. How hard must he throught the ball (m/s) for it to go into the hoop but not hit the backboard?
--

6. Sep 13, 2009

### rl.bhat

Re: Initial Velocity of a projectile, how???

This equation is correct.
But Vix is wrong. Check the calculation.

7. Sep 13, 2009

### free-node-5

Re: Initial Velocity of a projectile, how???

extreme thanks

I'm not sure what I did at this point because I failed so many times but when i fixed that mistake, I managed to get to a correct final solution