What is the maximum height this rocket will reach?

Equation: h= -5t^2+30t+10

Please show me how to do this

Question

What is the maximum height this rocket will reach?

Equation: h= -5t^2+30t+10

Please show me how to do this

unklerhaukus · Answer

Can you take the first derivative of h (with respect to t)?

ohohaye · Answer

What?

anonymous · Answer

Refer to the attachment from Mathematica.

whpalmer4 · Answer

No need for calculus if you remember a bit of analytic geometry.

If you have a parabola $$h = at^2 + bt + c$$the x-coordinate of the vertex (which will be the point of maximum height) is given by $$t= -\frac{b}{2a}$$That gives you the time at which the rocket is at the apex of the flight, and plugging that value into the formula for the height will give you the height at that point.

Here you have $$h = -5t^2+30t + 10$$so $a = -5, b = 30, c = 10$ and the time of maximum height is 
$$t = -\frac{b}{2a} = -\frac{30}{2(-5)} = 3$$Height at $t = 3$ is $$h(3) = -5(3)^2 + 30(3) + 10 = -45 + 90 + 10 = 55$$