Question

A boat moves with the stream of water from point A and B and it return back with the same speed. Velocity
of boat relative to water is n times the velocity of the water. Velocity of the water is 1m/sec. Find out the
average speed in the whole iternary
a) n -1
b) z? +1
c) 172
d) None of these​

Answer 1

Answer: A) n-1

Explanation: option A) n-1 because,

A boat moves with the flow of water from point A to point B and returns at the same speed.  The speed at which water flows is known as the velocity of water. Our online calculator resource determines the velocity of water in a pipe (when the flow rate and diameter of the pipe are known). Flow rates are usually measured by the volume of water passing per minute. The velocity of the boat in relation to the water is n times the velocity of the water. The water's velocity is one metre per second.

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Answer 2

Answer:

The correct answer is d) none of these

Concept:

• Relative velocity
• Frames of reference

Given:

• Velocity of water = 1m/s
• The velocity of the boat relative to water = n times velocity of water
• The velocity of the boat relative to water = n m/s
• The boat moves from point A to B and returns

Find:

• The average speed

Solution:

• Let the distance between A and B be D.
• While going from A to B, the boat is in the direction of the stream flow, so the relative velocity of the boat is the sum of the velocities of the boat and the water.
• Relative velocity of boat from A to B = (n+1)m/s
• The time taken from A to B = D/(n+1) s
• While going from B to A, the boat is in the direction of the stream flow, so the relative velocity of the boat is the difference of the velocities of the boat and the water.
• Relative velocity of boat from B to A = (n-1) m/s
• The time taken from B to A = D/(n-1) s
• Total time taken = [D/(n+1)]+[D/(n-1)]
• Total time taken = [D(n-1) + D (n+1)]/ (n-1)(n+1)
• Total time taken = (Dn-D+Dn+D)/(n-1)(n+1)
• Total time taken = 2Dn/(n-1)(n+1)
• Total distance covered = 2D
• Average speed = 2Dn/2D(n-1)(n+1)
• Average speed = n/(n-1)(n+1)

The average speed is n/(n-1)(n+1)

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