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
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.
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.
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!
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?