College Physics, Volume 1
College Physics, Volume 1
2nd Edition
ISBN: 9781133710271
Author: Giordano
Publisher: Cengage
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Chapter 1, Problem 74P

(a)

To determine

The maximum and minimum of A+B.

(a)

Expert Solution
Check Mark

Answer to Problem 74P

The maximum and minimum of A+B are 29m and 5m respectively.

Explanation of Solution

When the two vectors are in the same direction, A+B will be maximum. The maximum of A+B is given by,

    (A+B)max=|A|+|B|

When the two vectors are in the opposite direction, A+B will be minimum. The minimum of A+B is given by,

    (A+B)min=|B||A|

Conclusion:

Substitute 12 m for |A| and 17 m for |B| to get (A+B)max.

    (A+B)max=(12m)+(17m)=29m

Substitute 12 m for |A| and 17 m for |B| to get (A+B)min.

    (A+B)min=(17m)(12m)=5m

Therefore, the maximum and minimum of A+B are 29m and 5m respectively.

(b)

To determine

The maximum and minimum of AB.

(b)

Expert Solution
Check Mark

Answer to Problem 74P

The maximum and minimum of AB are 29m and 5m respectively.

Explanation of Solution

When the two vectors are in the opposite direction, AB will be maximum. The maximum of AB is given by,

    (AB)max=|A|(|B|)=|A|+|B|

When the two vectors are in the same direction, AB will be minimum. The minimum of AB is given by,

    (AB)min=|B||A|

Conclusion:

Substitute 12 m for |A| and 17 m for |B| to get (AB)max.

    (AB)max=(12m)(17m)=29m

Substitute 12 m for |A| and 17 m for |B| to get (AB)min.

    (AB)min=(17m)(12m)=5m

Therefore, the maximum and minimum of AB are 29m and 5m respectively.

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