Question

A toy rocket is launched from the top of a building 105 feet tall at an initial velocity of 163 feet per second. a) Give the function that describes the height of the rocket in terms of time t. b) Determine the time at which the rocket reaches its maximum height, and the maximum height in feet. c) For what time interval will the rocket be more than 433 feet above ground level? d) After how many seconds will it hit the ground? a) The function that describes the height of the rocket in terms of t is s(t) = b) The rocket reaches its maximum height of feet after approximately seconds. (Round to the nearest hundredth as needed.) Enter your answer in each of the answer boxes.

          A toy rocket is launched from the top of a building 105 feet tall at an initial velocity of 163 feet per second.
a) Give the function that describes the height of the rocket in terms of time t.
b) Determine the time at which the rocket reaches its maximum height, and the maximum height in feet.
c) For what time interval will the rocket be more than 433 feet above ground level?
d) After how many seconds will it hit the ground?
a) The function that describes the height of the rocket in terms of t is s(t) = 
b) The rocket reaches its maximum height of feet after approximately seconds.
(Round to the nearest hundredth as needed.)
Enter your answer in each of the answer boxes.

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A toy rocket is launched from the top of a building 105 feet tall at an initial velocity of 163 feet per second.
a) Give the function that describes the height of the rocket in terms of time t.
b) Determine the time at which the rocket reaches its maximum height, and the maximum height in feet.
c) For what time interval will the rocket be more than 433 feet above ground level?
d) After how many seconds will it hit the ground?
a) The function that describes the height of the rocket in terms of t is s(t) =
b) The rocket reaches its maximum height of feet after approximately seconds.
(Round to the nearest hundredth as needed.)
Enter your answer in each of the answer boxes.

Added by Gary J.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Kathleen Carty

03/31/2022

Step 1

Step 1:** The function that describes the height of the rocket in terms of time is: \[ s(t) = -16t^2 + 163t + 105 \] ** Show more…

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Transcript

00:01 Okay, so i have a toy rocket being launched from the top of a building 105 feet tall at an initial velocity of 163 feet per second.

00:11 So i've drawn the general form or written out the general form of a position function and now we're going to personalize it.

00:19 So for our problem, our initial velocity is 163 feet per second and our initial height is the height of the building 105.

00:28 So our function for part a will be s of t equals negative 16 t squared plus 163t because we're launching upward plus 105.

00:44 So that takes care of that.

00:47 Now in b, i want to know about maximum height.

00:52 Okay.

00:53 So maximum height is going to happen at the vertex of this parabola.

00:58 So the time for max height, i'm going to find by taking opposite of b, which in this case is 163 over 2a.

01:11 I'm finding the x coordinate of the vertex, opposite of b over 2a.

01:17 And when i do that, i'm going to get a time of approximately 5 .10 seconds.

01:26 Now, what max height is, well, that's the height i'm going to get when i put that 5 .1 seconds into my position function.

01:44 And that just becomes a calculator operation.

01:47 I find out that that is 520 .14 feet.

01:54 Okay.

01:57 In part c, i want to know for what time interval will the rocket be more than 433 feet? feet above ground level.

02:07 Okay.

02:08 So i'm going to set my function equal to 433.

02:22 I'm going to get everything on one side and zero on the other...

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