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During a fireworks display, a starburst rocket is shot upward with an initial velocity of 34.5 m/s from a platform 3.2 m high. The height, h, in meters, of the rocket after t seconds can be modelled by the function h(t) = −4.9t² + 34.5t + 3.2. a. Determine the velocity and acceleration of the rocket at 3 s. b. When the rocket reaches its maximum height, it explodes to create a starburst display. How long does it take for the rocket to reach its maximum height? C. At what height does the starburst display occur?

During a fireworks display, a starburst rocket is shot upward with an initial velocity of 34.5 m/s from a platform 3.2 m high. The height, h, in meters, of the rocket after t seconds can be modelled by the function h(t) = −4.9t² + 34.5t + 3.2. a. Determine the velocity and acceleration of the rocket at 3 s. b. When the rocket reaches its maximum height, it explodes to create a starburst display. How long does it take for the rocket to reach its maximum height? C. At what height does the starburst display occur?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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During a fireworks display, a starburst rocket is shot upward with an initial velocity of 34.5 m/s from a platform 3.2 m high. The height, h, in meters, of the rocket after t seconds can be modelled by the function h(t) = −4.9t² + 34.5t + 3.2. a. Determine the velocity and acceleration of the rocket at 3 s. b. When the rocket reaches its maximum height, it explodes to create a starburst display. How long does it take for the rocket to reach its maximum height? C. At what height does the starburst display occur? d. Sometimes the rockets malfunction and do not explode. How long would it take for an unexploded rocket to return to the ground? e. At what velocity would it hit the ground?
Transcribed Image Text:During a fireworks display, a starburst rocket is shot upward with an initial velocity of 34.5 m/s from a platform 3.2 m high. The height, h, in meters, of the rocket after t seconds can be modelled by the function h(t) = −4.9t² + 34.5t + 3.2. a. Determine the velocity and acceleration of the rocket at 3 s. b. When the rocket reaches its maximum height, it explodes to create a starburst display. How long does it take for the rocket to reach its maximum height? C. At what height does the starburst display occur? d. Sometimes the rockets malfunction and do not explode. How long would it take for an unexploded rocket to return to the ground? e. At what velocity would it hit the ground?
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