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Unit 5 Project 1. A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time I can be described by the polynomial function P(t) = -16ť + 3000 a. Find the height of the projectile when t = 1 second. b. Find the height of the projectile when t = 5 seconds. c. How long will it be until the object hits the ground? 2. A board has length (3x + 6x - 18) meters and width of 2x + 1 meters. The board is cut into three pieces of the same length a. Find the length of each piece. b. Find the area of each piece. c. Find the area of the board before it is cut. d. How is the area of each piece of the board related to the area of the board before it is cut? 3. A cubic equation has zeros at -2, 1, and 3. a. Write an equation for a polynomial function that meets the given conditions. b. Draw the graph of a polynomial function that meets the given conditions. 4. Alice was having a conversation with her friend Trina, who had a discovery to share: 10

Unit 5 Project 1 A Projectile Is Fired Upward From The Ground With An Initial Velocity Of 300 Feet Per Second Neglecting Air Resistance The Height Of The Projec class=

Sagot :

1)

The polynomial modelling this scenario is expressed as

P(t) = - 16t^2 + 300t

where

P(t) represents the height at time t

a) To find the height of the projectile when t = 1 second, we would substitute

t = 1 into the equation. Thus,

P(1) = - 16(1)^2 + 300(1)

P(1) = - 16 + 300 = 284

Height of projectile when t = 1 second is 284 feet

b) To find the height of the projectile when t = 5 second, we would substitute

t = 5 into the equation. Thus,

P(1) = - 16(5)^2 + 300(5)

P(1) = - 400 + 1500

Height of projectile when t = 5 second is 1100 feet

c) At the time when the object hits the ground, the height would be zero. This means that p(t) = 0

Thus, the equation would be

0 = - 16t^2 + 300t

Factoring out 4t from the right, we have

0 = - 4t(4t - 75)

- 4t = 0 or 4t - 75 = 0

t = 0/-4 or 4t = 75

t = 0 or t = 75/4

t = 0 or t = 18.75

It will take 18.75 seconds until the object hits the ground

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