The height above ground of a snowball thrown from a cliff is modeled by the function h(t) = -16t2 + 64t + 192, where h is height in feet and t is time in seconds.

Question

The height above ground of a snowball thrown from a cliff is modeled by the function h(t) = -16t2 + 64t + 192, where h is height in feet and t is time in seconds.

I d3on't know what to do with this i use to do this but know i forgot
Guide me through this please

👇

4 answers
(click or scroll down)

👇

Answer 1

Reiny answered
7 years ago

What's the question?

If you want the maximum height:
the vertex will tell you how high it went and how long it took to reach that height.

the t of the vertex is -64/(-32) = 2 seconds
h(2) = -64 + 128 + 192 = 256 ft above the ground
(the vertex was (2, 256)

when will it hit the ground?
0 = -16t^2 + 64t + 192
t^2 - 4t - 12 = 0
(t-6)(t+2) = 0
t = 6 or t = -2, the last answer makes no sense.

Answer 2

Edward Burger answered
2 years ago

First you must find the vertex. The vertex is -64/(-32) = 2 seconds

h(2) = -64 + 128 + 192 = 256
V = (2/256)

To find the vertex the formula f(x) = ax^2 +bx + c must be used.

Answer 3

Step-by-Step Bot answered
1 year ago

Sure! Let's break down the problem step by step.

Step 1: Understand the given information.
We are given a function h(t) = -16t^2 + 64t + 192, where h represents the height above the ground and t represents time in seconds. The coefficient -16 in front of t^2 represents the effect of gravity on the snowball.

Step 2: Find the maximum height.
To find the maximum height of the snowball, we need to determine the vertex of the parabolic function. The formula for finding the vertex of a quadratic function in the form ax^2 + bx + c is given by x = -b/2a. In our case, a = -16 and b = 64.

Using the formula, we have:
t = -64 / (2 * -16)
t = -64 / -32
t = 2

The maximum height occurs when t = 2 seconds.

Step 3: Substitute the value of t into the equation to find the maximum height.
To find the maximum height, substitute t = 2 back into the original equation h(t):
h(2) = -16(2)^2 + 64(2) + 192
h(2) = -64 + 128 + 192
h(2) = 256

So, the maximum height of the snowball above the ground is 256 feet.

Step 4: Analyze the motion of the snowball.
Since the coefficient of t^2 is negative (-16), the parabolic function is concave down. This means that the snowball will reach a maximum height at t = 2 seconds and then start to descend.

Step 5: Answer any specific questions or additional steps.
If you have any further questions or need assistance with specific parts of the problem, feel free to ask!

Answer 4

Explain Bot answered
11 months ago

Sure! I can guide you through this problem step by step.

To find the height above the ground over time, we will evaluate the given function.

The function provided is h(t) = -16t^2 + 64t + 192.

To find the height at a specific time, substitute the value of t into the function.

Let's say we want to find the height at t = 2 seconds.

Step 1: Substitute the value of t into the function:
h(2) = -16(2)^2 + 64(2) + 192

Step 2: Simplify the equation using the order of operations (PEMDAS/BODMAS):
h(2) = -16(4) + 128 + 192
h(2) = -64 + 128 + 192
h(2) = 256

The height of the snowball at t = 2 seconds is 256 feet.

Similarly, you can substitute different values of t into the function to find the height at different times.

Is there anything else you would like to know about this topic?