Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 8.7, Problem 8CFU

To determine

To find: the parametric equations that represent the path of probes.

Expert Solution

Answer to Problem 8CFU

$x=440ty=−16t2+3500$

Explanation of Solution

Given information:

Height $(h)=3500 feet$

Initial velocity $(v→)=330 mph$

Path of plane is parallel to the ground at the time of releasing the probes, so $θ=0°$ .

Calculation:

First convert the velocity into feet per second as follows:

$|v→|=330 mph(5280 feet1 mile)(1 hour3600 s)=440 feet per second$

Now solve the horizontal and vertical components as shown below.

$x=t|v→|cosθ=t(440)cos0° [Put the value of |v→| and θ]=440t$

$y=t|v→|sinθ−12gt2+h=t(440)sin0°−12(32)t2+3500 [Put the value of |v→|,g,h and θ]=−16t2+3500$

Thus the parametric equations are $x=440t$ and $y=−16t2+3500$ .

To determine

To graph: the parametric equations that represent the path of probes.

Expert Solution

Explanation of Solution

Given information:

Parametric equations evaluated in part a. are shown below.

$x=440ty=−16t2+3500$

Calculation:

Express $t$ in terms of $x$ as shown below.

$x=440tt=x400$

Now substitute the value of $t$ in parametric equation for $y$ as follows:

$y=−16t2+3500=−16(x400)2+3500$

Create a table of values for $x and y$ as shown below.

$x$	0	1000	2000	3000	4000	5000	6000	6507
$y$	3500	3417.3	3169.4	2756.2	2177.7	1433.8	524.8	0.7

Plot the points and join them with a soft curve to get the graph of given parametric equations as shown below.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 8.7, Problem 8CFU

To determine

To find: the time taken by the probes to reach the ground.

Expert Solution

Answer to Problem 8CFU

14.8 seconds

Explanation of Solution

Given information:

Parametric equations evaluated in part a. are shown below.

$x=440ty=−16t2+3500$

Calculation:

When the probe will reach the ground the value of $y$ will become zero. Substitute $y=0$ in the equation for $y$ and solve $t$ as shown below.

$y=−16t2+35000=−16t2+3500 [Put y=0]16t2=3500 [Add 16t2 on each side]t2=350016 [Divide each side by 16]t=350016 [Taking square roots on each side]=14.8 seconds$

Thus the required time taken by probe to reach the ground is 14.8 seconds.

To determine

To find: the horizontal distance travelled by probes before hitting the ground.

Expert Solution

Answer to Problem 8CFU

$6214 feet$

Explanation of Solution

Given information:

Parametric equations evaluated in part a. are shown below.

$x=440ty=−16t2+3500$

Time taken to reach the ground $(t)=14.8 seconds$

Calculation:

Substitute the value of $t$ in parametric equation for $x$ and solve as follows:

$x=440t=440(14.8)=6214 feet$

Thus the horizontal distance travelled by probes before hitting the ground is 6215 feet.

Chapter 8.7, Problem 7CFU

Chapter 8.7, Problem 9E

Chapter 8 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 8.1 - Prob. 1CFU Ch. 8.1 - Prob. 2CFU Ch. 8.1 - Prob. 3CFU Ch. 8.1 - Prob. 4CFU Ch. 8.1 - Prob. 5CFU Ch. 8.1 - Prob. 6CFU Ch. 8.1 - Prob. 7CFU Ch. 8.1 - Prob. 8CFU Ch. 8.1 - Prob. 9CFU Ch. 8.1 - Prob. 10CFU

Ch. 8.1 - Prob. 11CFU Ch. 8.1 - Prob. 12CFU Ch. 8.1 - Prob. 13CFU Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Prob. 40E Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Prob. 45E Ch. 8.1 - Prob. 46E Ch. 8.1 - Prob. 47E Ch. 8.1 - Prob. 48E Ch. 8.1 - Prob. 49E Ch. 8.1 - Prob. 50E Ch. 8.1 - Prob. 51E Ch. 8.1 - Prob. 52E Ch. 8.2 - Prob. 1CFU Ch. 8.2 - Prob. 2CFU Ch. 8.2 - Prob. 3CFU Ch. 8.2 - Prob. 4CFU Ch. 8.2 - Prob. 5CFU Ch. 8.2 - Prob. 6CFU Ch. 8.2 - Prob. 7CFU Ch. 8.2 - 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