# Projectile to hit x,y from x,y given max height

1. Jul 27, 2009

### Ehdrian

Hello!

This is not homework :-)

I can figure this out:
Code (Text):

y = 100 = max height

0,0                                                  200,0
------------------------------------------------------------
By getting the initial y velocity = sqrt(2 * gravity * max height)
and time to peak height = initial_y_velocity / gravity
and the initial x velocity = distance_x / (time_to_peak_height * 2);

However, I need to hit a point with elevation such as:
Code (Text):

y = 100 = max height
190,65
-----------------

0,0
-------------------------------------------
So, given max height, start point, and end point. What is my initial velocity x, and initial velocity y? No wind, and gravity is constant.

I've really come to a stand still on this! Any help would be great.

Adrian

2. Jul 27, 2009

### Ja4Coltrane

I had a little bit of trouble understanding this but I'm assuming you want the initial velocity that gives a max height of 100 and crosses the point (190,65).

There are probably several approaches but here is what comes to mind:

1) Write y = ax^2 + bx (no need for an extra + c since y(x=0) = 0)

2) Note that y_max = 100 so y(x=-b/2a) = 100. This gives an equation for b in terms of a.

3) set 65 = a*(190)^2 + b*(190), substitute b with the result of step 2. This gives you the value of a, and from part 2, you can find b.

4) Now you know the path exactly, from here, you can v_x by considering the max x distance (-b/a). You already know v_y from the max height.

Remember that there are two solutions!

Does this help?

3. Jul 27, 2009

### Staff: Mentor

It is still homework/coursework-like, so it belongs in the HH forums, where I've moved it.

Also, the same rules apply -- you must show us your attempt at a solution, and list the relevant equations. Please show us that work so that we can offer some tutorial advice.

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