General Physics, 2nd Edition
General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 25, Problem 29E

(a)

To determine

The time taken by boat upstream.

(a)

Expert Solution
Check Mark

Answer to Problem 29E

The time taken by boat upstream is 5hours.

Explanation of Solution

Write the expression for time during upstream.

  tu=dvbvw        (I)

Here, d is the distance between two islands, vb is velocity of boat, vw is velocity of water and tu is time required during upstream.

Conclusion:

Substitute 5kmh1 for vb, 3kmh1 for vw and 10km for d in equation (I).

  tu=10km5kmh13kmh1=5h

Thus, the time taken by boat upstream is 5hours.

(b)

To determine

The time taken by boat downstream.

(b)

Expert Solution
Check Mark

Answer to Problem 29E

The time taken by boat downstream is 1.25hours.

Explanation of Solution

Write the expression for time during downstream.

  td=dvb+vw        (II)

Here, td is time required during downstream.

Conclusion:

Substitute 5kmh1 for vb, 3kmh1 for vw and 10km for d in equation (II).

  td=10km5kmh1+3kmh1=1.25h

Thus, the time taken by boat upstream is 1.25hours.

(c)

To determine

The time taken in total round trip.

(c)

Expert Solution
Check Mark

Answer to Problem 29E

The time taken in total round trip is 6.25hours.

Explanation of Solution

Write the expression for total time.

  t=td+tu        (III)

Here, t is time taken in total round trip.

Conclusion:

Substitute 1.25hours for td and 5hours for tu in equation (III).

  t=1.25hours+5hours=6.25hours

Thus, the time taken in total round trip is 6.25hours.

(d)

To determine

The time taken by boat in still water for round trip.

(d)

Expert Solution
Check Mark

Answer to Problem 29E

The time taken by boat in still water for round trip is 4hours.

Explanation of Solution

Write the expression for time by boat in still water.

  ts=2dvb        (IV)

Here, ts is time taken by boat in still water.

Conclusion:

Substitute 5kmh1 for vb and 10km for d in equation (IV).

  t=2(10km)5kmh1=4h

Thus, the time taken by boat in still water for round trip is 4hours.

(e)

To determine

The analogy between results and equation 25.1.

(e)

Expert Solution
Check Mark

Answer to Problem 29E

The time taken by object decreases when its speed increases when observed by observer.

Explanation of Solution

The above results also show that time taken by boat decreases when the boat moves downstream. Equation 25.1 gives the relation between actual time taken and time dilation.

Write the expression for time dilation.

  t=t1(u/c)2

Here, t is the time taken by light, t is the time taken by required by object, u is the speed of object and c is the speed of light in vacuum.

The time required by object moving at speed u will be more observed by person on the Earth than its actual time. However, t and t will be equal when the object moves at a speed of light.

Conclusion:

Thus, the time taken by object decreases when its speed increases when observed by observer.

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