Question

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The function H(t)=-16t^2+vt+s shows the height H(t), in feet, of projectile launched vertically from s feet above the ground after t seconds. The initial speed is v feet per second.

Part A: The projectile was launched from a height of 82 feet with an initial velocity of 60 feet per second. Create an equation to find the time taken by the projectile to fall on the ground.

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

(Part C and D will be in comments)

Answer 1

Part C: Another object moves in the air along the path of g(t)=10+63.8t where g(t) is the height, in feet, of the object from the ground at time t seconds.

Use a table to find the approximate solution to the equation H(t)=g(t) and explain what the solution represents in the context of the problem. [Use the function H(t) obtained in Part A and estimate using integer values]

Part D: Do H(t) and g(t) interest when the projectile is going up or down, and how do you know?

Answer 2

I'm not certain of my answers and do not understand what C is looking for, so here is my attempt for A and B.

A
H(t)=-16t^2+60t+82
You replace H(t) with 0 to find when it falls on the ground.

B
H'(t)=v(t)=-32t+60
t=15/8
H(15/8)=138.25 ft

Answer 3

ok well I think the sentence under Part C is for Part C.

Answer 4

If I put the formulas in a table, at t=2 , H(t)=138 and g(t)=137.6

Answer 5

what do u mean "if"

Answer 6

I had no specific reason for using the word "if"
I could have said "when" or something
I'm using a graphing calculator to make the table for me

Answer 7

C
Using a table, I find that g(t)=H(t) at approximately (2, 138)
This solution represents where and when the two objects will be at the same height. On a graph, this would be where the two lines intersect.
I double checked this by using my graphing calculator to calculate where they intersect. It gave me (2.0058915, 137.97588)

D
When the two objects intersect, the projectile is going up. I know because the maximum height that the projectile will reach is 138.25. This number is higher than the point of intersection, meaning that the projectile has yet to begin falling.

Answer 8

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