Question

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 100 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. (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) = 20 + 38.7t where g(t

Answer 1

he 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

@YanaSidlinskiy

Answer 3

@iPwnBunnies

Answer 4

I think for part A, the acceleration is the second derivative of position.

Maximum height occurs when the instantanous velocity is zero. So you take the first derivative and equate it to zero.

The third part is incomplete.

Answer 5

Part C: Another object moves in the air along the path of g(t) = 20 + 38.7t 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)

Answer 6

Could you explain part A?

Answer 7

Is this question in physics or math? Calculus one?

Answer 8

math, algebra 1

Answer 9

Oh..... I way over thought this problem sorry.

Answer 10

hahahaha its okay. i don't understand it at all so.

Answer 11

For the first part, it is stated that the height is 100 feet and initial velocity is 60 feet per second.

So, in order to get to time, you can plug these values in the formula. h(t) = 100 and v = 60.

Can you see what I am talking about?

Answer 12

whats the formula?

Answer 13

Its given. The first one on top.

Answer 14

oh wait never mind, let me try it.

Answer 15

So it will be:

100 = -16t^2 +60t + s.

So far so good?

Answer 16

yes

Answer 17

Can you solve for t?

Answer 18

wouldn't you need s?

Answer 19

Its not given, dont worry about it.

Answer 20

okay so it would be

Answer 21

Okay good.

Now, for part B, the total time to get there is half of this so you take this value and divide it by 2.

After doing that you take and put it the equation you got for part A for t, and then you solve for s. This will give you the maximum height reached.

Answer 22

No the value of the t divided by 2.

You plug that value into this formula and you solve for s.