Hard Math problem! See if you can solve!?

Question

The height, in feet, of a missile is given by H= 1600t-16t^2 and the t is the time in seconds.

A) What is the maximum height reached by the missile??
B) What is the time it reaches the maximum height??
C) What is the time when the missile hits the ground??

Explain the answers!!
Thax!

Answer 1

This is the equation of a parabola.
The max height is the y value of the vertex.
The time is the x value of the vertex.

Put in standard form -16t^2 + 1600t +0 = 0
-1600/-32 (-b/2a) is the x value = time = 50 sec.
at X=50, Y= 40,000 feet.
The missle hits the ground at 100 seconds, because max height is halfway through its travel

Answer 2

Solve B first: Take the first derivative of the equation and set it equal to zero. The first derivative is 1600 - 32t, so t=1600/32=50

Solve A by putting 50 into the equation.

Solve C by setting the equation equal to zero and solving.

Answer 3

A) -b /2a
-1600 /(2*-16)
1600(50)-16(50)^2
H= 40,000ft

B) 50s

C) 100s