Question

Help me out with a lengthy question?

Answer 1

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? Show your work. (2 points)

Part C: Another object moves in the air along the path of g(t) = 28 + 48.8t 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] (4 points)

Part D: Do H(t) and g(t) intersect when the projectile is going up or down, and how do you know? (2 points)

Answer 2

For A, replace v with 50 and s with 9.
B, solve plug in -b/2a = -50/32 into H(t)
C, Set H(t) = g(t) and solve.
D, Check the slope at that point

Answer 3

For A use what formula? H(t) = -16t^2 + vt + s?

Answer 4

Yeah.

Answer 5

I got the equation,

H(t) = -16t^2 + 50t + 9

This is a quadratic equation, correct?

How do I solve it?

Answer 6

Scratch that, not a Quadratic Equation, but I still can't solve it.

Answer 7

It's quadratic.
You can use the formula.

Answer 8

Confirming: \[h(t)=-16t^2 + v _{0}t +s _{0} \]definitely is a quadratic function. Note that you really do need to use those subscripts to indicate initial velocity and initial position (height above the ground). v and s without subscripts are variables, whereas \[v _{0}~and~s _{0}\] are initial values (which are in turn, constants).

Answer 9

What do you believe you still need to pick up / learn / do to finish solving this problem?