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A diver jumps off a spring board that is 10 feet above the water. The board throws the diver up with an upward velocity of 9 feet per second. Eventually, gravity over comes the force of the diving board and the the diver begins to come down. The diver is thrown into the air fairly quickly, he slows down until he stops, then begins to come back down (slowly at first, then faster and faster until he hits the water).

The height of any object like the diver that is projected into the air can be modeled with the following function:

h(t) = -16t^2 + v*t + m

In this function:

h(t) is the height of the object t seconds after it was thrown into the air.

t is the number of seconds after the object was thrown in the air.

v is the initial upward velocity (for the diver this was 9 ft per second).

m is the initial height of the object (for the diver this is 10 feet).


Question #1


What does the v*t represent in the case of the diver?


Question #2


What do you think the -16t^2 represents in the case of the diver?


Question #3


How high will the diver be 1 second after he leaves the board (find h(1))?


Question #4 Now


What will h(t) be when the diver hits the water?


Question #5 Now


How long will it take the diver to hit the water (Hint: Put 0 in for h(t), then solve for t)?

Respuesta :

MrRoyal

The diver will be 3 feet high 1 second after he leaves the board and the diver will hit the water after 1.12 seconds

What does the v*t represent in the case of the diver?

The function is given as:

h(t) = -16t^2 + v*t + m

The variable v represents the velocity, while the variable t represents time

So, we have:

v * t = velocity * time

v * t = distance

Hence, v*t in the case of the diver represents distance

What do you think the -16t^2 represents in the case of the diver?

We have:

-16t^2

Where

a = -16 --- the acceleration

The variable t represents time

So, we have:

-16t^2 = -16 * time squares

-16t^2 = distance

Hence, -16t^2 in the case of the diver represents distance

How high will the diver be 1 second after he leaves the board?

To do this, we calculate h(1).

So, we have:

h(t) = -16t^2 + v*t + m

This gives

h(t) = -16t^2 + 9*t + 10

This gives

h(1) = -16 * 1^2 + 9*1 + 10

Evaluate

h(1) = 3

Hence, the diver will be 3 feet high 1 second after he leaves the board

What will h(t) be when the diver hits the water?

Here, we set h to 0

-16t^2 + 9*t + 10 = 0

Using a graphing calculator, we have:

t = 1.12

Hence, the diver will hit the water after 1.12 seconds

Read more about height functions at:

https://brainly.com/question/12446886

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