Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

1st Edition

ISBN: 9781680331165

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 2.1, Problem 44E

To determine

Describe the transformation of the graph of f to obtain g . Further, find the height from which the object should be dropped on the moon, so it hits the ground the same time as on Earth.

Expert Solution & Answer

Answer to Problem 44E

The function g is obtained when the function f is vertically shrinked by a factor of 16.

The height from which the object should be dropped on the moon, so it hits the ground the same time as on Earth is 1.67 feet.

Given Information: The function f(t)=−16t2+10 models the height of an object t seconds after it is dropped from a height of 10 feet on earth. The function g(t)=−83t2+10 models the height of an object t seconds after it is dropped from a height of 10 feet on the moon.

Calculation:

The height of both the objects that fall from earth or moon is same. The only difference between both the functions is that of the prefix of t2 . The function g can be obtained by a vertical shift in the function of f . That is,

f(t)=−16t2+10=(16)−16t2+10=−83t2+10=g(t)

Hence, the function g is obtained when the function f is vertically shrinked by a factor of 16 .

When the object reaches ground, height becomes 0. That is, f(t)=0 .

The time taken by the object to reach the ground on earth is,

f(t)=0−16t2+10=0−16t2=−10t2=1016=58 ...... (1)

When the object on moon reaches ground, the height becomes 0. That is, g(t)=0 .

If the time taken by the object on moon to reach the ground at the same time as that of the object thrown on earth the time should be equal to that obtained in equation (1).

That is, t2=58

Now substitute all these values in the model g(t)=−83t2+h to obtain theheight from which the object should be dropped.

Here, h represents the height from which the object should be dropped on the moon, so it hits the ground the same time as on Earth.

g(t)=−83t2+h0=(−83)(58)+hh=53≈1.67

Hence, the height from which the object should be dropped on the moon, so it hits the ground the same time as on Earth is 1.67 feet.

Explanation of Solution

Calculation:

f(t)=−16t2+10=(16)−16t2+10=−83t2+10=g(t)

Hence, the function g is obtained when the function f is vertically shrinked by a factor of 16 .

When the object reaches ground, height becomes 0. That is, f(t)=0 .

The time taken by the object to reach the ground on earth is,

f(t)=0−16t2+10=0−16t2=−10t2=1016=58 ...... (1)

When the object on moon reaches ground, the height becomes 0. That is, g(t)=0 .

If the time taken by the object on moon to reach the ground at the same time as that of the object thrown on earth the time should be equal to that obtained in equation (1).

That is, t2=58

Now substitute all these values in the model g(t)=−83t2+h to obtain theheight from which the object should be dropped.

Here, h represents the height from which the object should be dropped on the moon, so it hits the ground the same time as on Earth.

g(t)=−83t2+h0=(−83)(58)+hh=53≈1.67

Hence, the height from which the object should be dropped on the moon, so it hits the ground the same time as on Earth is 1.67 feet.

Chapter 2.1, Problem 43E

Chapter 2.1, Problem 45E

Chapter 2 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - Prob. 51E Ch. 2.1 - Prob. 52E Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - 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