Homework Help: Parabolic motion

1. Nov 2, 2015

PhoenixWright

• Member warned to use the formatting template for homework posts.
I have a problem that means:

The jet of water from a fire hose comes with a vo speed. If the hose nozzle is located at a distance d from the base of a building, demostrate that the nozzle should be tilted at an angle such that $$tan \alpha = \frac{v_0^2}{gd}$$

so that the jet strikes the building as high as possible. At the point where it hits, is the jet is going up or going down?
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I have tried this:

If the jet reaches the building as high as possible:

$$v_y = 0,$$ so $$t = \frac{v_0 sin \alpha}{g}$$

When the jet reaches the building, x = d, so:

$$x = v_0 cos \alpha t \\ t = \frac {d}{v_0 cos \alpha}$$

I have, therefore:

$$\frac{v_0 sin \alpha}{g} = \frac {d}{v_0 cos \alpha} \\ \frac{v_0^2}{gd} = \frac{1}{cos \alpha sin \alpha}$$

I should have $$tan \alpha$$ where I have $$\frac{1}{cos \alpha sin \alpha}$$

What is it wrong?

Thank you!

2. Nov 2, 2015

haruspex

Certainly that will be the case at the highest point of the trajectory, for a given angle, but that leaves open the possibility that a higher point could be reached at the given distance by using a different angle. In other words, you have assumed the jet will be horizontal at the target.
(Not saying this is wrong, merely that you have not demonstrated it.)

3. Nov 2, 2015

PhoenixWright

Thank you!

Then, I think I should add a condition more (one equation), but I have no idea what it is. If I add $$y = h_0 + v_0sin \alpha t -1/2 gt^2$$, I would have h unknown; and I think I don't have more equations...

4. Nov 2, 2015

haruspex

You can substitute for t in there using the equation you had from the X direction. It remains to maximise y wrt alpha.

5. Nov 3, 2015

PhoenixWright

Thank you! Now I understand it.