a. Answer The required time for which the fish has to swim away is 0.97 seconds. Explanation Given information: The initial height, h 0 = 100 feet The initial vertical velocity, v 0 = − 88 feet per second Formula used: Quadratic formula : x = − b ± b 2 − 4 a c 2 a Calculation: The initial height is h 0 = 100 feet. The initial vertical velocity is v 0 = − 88 feet per second. To find the required time, use the equation h = − 16 t 2 + v 0 t + h 0 . Substitute − 88 for v 0 , 100 for h 0 and 0 for h in the above equation. 0 = − 16 t 2 − 88 t + 100 − 16 t 2 4 − 88 t 4 + 100 4 = 0 4 − 4 t 2 − 22 t + 25 = 0 4 t 2 + 22 t − 25 = 0 To solve the above equation for t , use the formula x = − b ± b 2 − 4 a c 2 a . t = − 22 ± 22 2 − 4 ( 4 ) ( − 25 ) 2 ( 4 ) = − 22 ± 484 + 400 8 = − 22 ± 884 8 = − 22 ± 2 221 8 Solve for t . t = − 22 ± 2 221 8 t = − 11 ± 221 4 Now, t = − 11 + 221 4 = − 11 + 14.86 4 = 0.965 ≈ 0.97 And, t = − 11 − 221 4 = − 11 − 14.86 4 = − 6.465 But time cannot be negative. Hence, the required time for which the fish has to swim away is 0.97 seconds. b. To determine The bird which will reach the fish first. Answer The first bird will reach the fish first. Explanation Given information: The initial height, h 0 = 84 feet The initial vertical velocity, v 0 = − 70 feet per second Formula used: Quadratic formula: x = − b ± b 2 − 4 a c 2 a Calculation: The initial height is h 0 = 84 feet. The initial vertical velocity is v 0 = − 70 feet per second. To find the required time, use the equation h = − 16 t 2 + v 0 t + h 0 . Substitute − 70 for v 0 , 84 for h 0 and 0 for h in the above equation. 0 = − 16 t 2 − 70 t + 84 16 t 2 2 + 70 t 2 − 84 2 = 0 2 8 t 2 + 35 t − 42 = 0 To solve the above equation for t , use the formula x = − b ± b 2 − 4 a c 2 a . t = − 35 ± 35 2 − 4 ( 8 ) ( − 42 ) 2 ( 8 ) = − 35 ± 1225 + 1344 16 = − 35 ± 2569 16 Solve for t . t = − 35 + 2569 16 t = − 35 + 50.68 16 t = 15.68 16 t = 0.98 And, t = − 35 − 2569 16 t = − 35 − 50.68 16 t = − 85.68 16 t = − 5.355 But time cannot be negative. So, the time is 0.98 seconds. Hence, the first bird will reach the fish first.

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

See similar textbooks

Question

Chapter 3.4, Problem 67E

To determine

To calculate: The time for which the fish has to swim away.

Expert Solution

Answer to Problem 67E

The required time for which the fish has to swim away is 0.97 seconds.

Explanation of Solution

Given information:

The initial height, h0=100 feet

The initial vertical velocity, v0=−88 feet per second

Formula used:

Quadratic formula:

x=−b±b2−4ac2a

Calculation:

The initial height is h0=100 feet.

The initial vertical velocity is v0=−88 feet per second.

To find the required time, use the equation h=−16t2+v0t+h0 .

Substitute −88 for v0 , 100 for h0 and 0 for h in the above equation.

0=−16t2−88t+100−16t24−88t4+1004=04−4t2−22t+25=04t2+22t−25=0

To solve the above equation for t , use the formula x=−b±b2−4ac2a .

t=−22±222−4(4)(−25)2(4)=−22±484+4008=−22±8848=−22±22218

Solve for t .

t=−22±22218t=−11±2214

Now, t=−11+2214=−11+14.864=0.965≈0.97

And, t=−11−2214=−11−14.864=−6.465

But time cannot be negative.

Hence, the required time for which the fish has to swim away is 0.97 seconds.

To determine

To determine: The bird which will reach the fish first.

Expert Solution

Answer to Problem 67E

The first bird will reach the fish first.

Explanation of Solution

Given information:

The initial height, h0=84 feet

The initial vertical velocity, v0=−70 feet per second

Formula used:

Quadratic formula:

x=−b±b2−4ac2a

Calculation:

The initial height is h0=84 feet.

The initial vertical velocity is v0=−70 feet per second.

To find the required time, use the equation h=−16t2+v0t+h0 .

Substitute −70 for v0 , 84 for h0 and 0 for h in the above equation.

0=−16t2−70t+8416t22+70t2−842=028t2+35t−42=0

To solve the above equation for t , use the formula x=−b±b2−4ac2a .

t=−35±352−4(8)(−42)2(8)=−35±1225+134416=−35±256916

Solve for t .

t=−35+256916t=−35+50.6816t=15.6816t=0.98

And, t=−35−256916t=−35−50.6816t=−85.6816t=−5.355

But time cannot be negative.

So, the time is 0.98 seconds.

Hence, the first bird will reach the fish first.

Chapter 3.4, Problem 66E

Chapter 3.4, Problem 68E

Chapter 3 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

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