Question

Could Someone Pretty Please help me! :(

The function H(t) = -16t2 + vt + s shows the height H (t), in feet, of a projectile launched vertically from s feet above the ground after t seconds. The initial speed of the projectile is v feet per second.

Part A: The projectile was launched from a height of 90 feet with an initial velocity of 50 feet per second. Create an equation to find the time taken by the projectile to fall on the ground. (2 points)

Part B: What is the maximum height that the projectile will reach?

Answer 1

Hi.

You're given that \(H(t) = -16t^2 + vt + s\) is the equation of a projectile launched vertically \(s\) feet above the ground after \(t\) seconds with velocity \(v\).

In this question, \(v = 50\) and \(s = 90\). So your projectile would become something like\[H(t) = -16t^2 + 50 t + 90\]

Answer 2

okay so 50 is the speed and 90 is the hight

Answer 3

so for A it says to create an equation

Answer 4

We already have created the equation.

Answer 5

okay

Answer 6

but what would be the maximum height

Answer 7

im sorry its kind of confusing for me

Answer 8

\[H(t) = -16t^2 + 50t + 90\]Have you heard of any of these terms:
• Completing the square in a quadratic.
• Vertex of a quadratic.
• Calculus.

We can use any of the three to find out the maximum height.

Answer 9

Do you know calculus?

If not, we'll use the vertex of this quadratic.

Answer 10

OK, the vertex in that case.

The vertex of a quadratic is the point at which the maximum/minimum occurs. So does that tell you how we can use it?

Answer 11

Hmm...

Do you know what the vertex of a quadratic is?

Answer 12

If I give you a quadratic's graph, can you tell where the vertex is?

Answer 13

If I give you the graph of a quadratic, can you tell me where the vertex is?

Answer 14

i know a rectangle dont have a vertex

Answer 15

...hmm...

if I give you a function like \(H(t)\), how would you calculate its maximum value?