Question

A projectile is fired straight upward with an initial velocity of 400 feet per second. The height of the projectile, h(t), if represented by the function h(t)=-16t^2+400t, where t is the time in seconds. How long does it take the projectile to reach the maximum height?

Answer 1

Answer:

You can find the answer by using the formula x=-b/2a

Step-by-step explanation:

Remember the maximum height will be at the vertex. The x value of the vertex is your time, so use x=-b/2a. Then if it had also asked what the height was, you would plug that answer into your equation to find the y value of the vertex. Pretty sure your teacher is just asking you to find the x though:)

Answer 2

Answer:

We have to find te vertex of the parabola.

Given a square function:

F(x)=ax²+bx+c

The vertex of the parabola would be the point (-b/2a, f(-b/2a)

In cases like this:

h(t)=-16t²+576t

a=-16

b=576

-b/2a=-576/-32=18

h(18)=-16(18)²+576(18)=-5184+10368=5184

The vertex will be: (18, 5184)

Just because a is negative we've a maximum, in case a were positive the very least is had by us. we have the very least at t=18 s

Then; and the utmost heigth would be 5184 m

Answer: The projectile try reach it has the maximum heigth in 18 s, and the utmost level would be 5184 m.