How high is the stone at its highest? Relationships are given

Mushroom79

1. The problem statement, all variables and given/known data

A rock moves so that its coordinates at the time t given by the relationships

x=25t
y=20t-5t^2

How high is the stone at its highest?

2. Relevant equations

-

3. The attempt at a solution

I got the distance the stone flies (horizental ground) by setting y=0, that gave x=100m
If that is correct, how should I proceed?

voko

What curve is y with regard to t?

Mushroom79

A quadratic curve?

voko

Yes it is. You know the two points where it meets the t axis. What can be said about the location of its peak?

Mushroom79

It's above and between the two points.

voko

So as you know it's exactly midway, you know the value of t to plug into the equation and get the height.

Mushroom79

So I take the value of t I got from finding out the flying distance and divide it by 2?

If that is correct I got my answer! Thank you.

voko

Well, you could do it the "proper" way by taking the derivative, equating it to zero, etc.

But since you already know the roots of the equation, you can use the fact that the apex of the parabola is always right in the middle.

HallsofIvy

I would not consider taking the derivative to be the "proper" way for a problem like this. Rather, complete the square, so you get something like y= h- (x- a)^2. That is h when x= a, h minus something otherwise. That is, y= h is the maximum value of y.