What’s the maximum and the value of x?

Question

A rocket is fired from the top of a tower 100 feet high with an initial speed of 208 feet per second and at an angle of 45 degree to the horizontal, The height h in feet of the rocket above the level ground is given by h(x) =-0.00074x² +x+100, where x is the total distance from the base of the tower.

a) Find the maximum height of the rocket

b) How far (the x value) will the rocket reach the ground ?

Answer 1

Parabola h(x) is looking down, so it has a maximum at the vertex.

Vertex formula is -b/2a: -1/(2* (-0.00074)) which is equal to 675.68

a) Find the maximum height of the rocket is h(675.68) = -0.00074 * 675.68^2 + 675.68 + 100 = 437.84

b) How far (the x value) will the rocket reach the ground ?

At the point of contact h=0

So we have an equation

0 = -0.00074 x^2 +x + 100

Solving using quadratic formula gives 1444.88