Question

2. The width of the river is 1 km and velocity of river water is 5 km/hr. There are two boats at the same point on the bank. The velocity of each boat in still water is 10 km/hr. One of the boat starts its journey along the bank, it travels a distance 1 km upstream, and return back. Simultaneously, another boat starts its journey to the other bank by shortest path and returns back. Which of the boat returns to the starting point first?​

Answer 1

Explanation:

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Answer 2

Given:

The width of the rive r= 1 km

The velocity of river water = 5 km/hr

The velocity of each boat in still water = 10 km/hr

Boat A travels 1km upstream and comes back

Boat B travels to another bank via the shortest distance and comes back

To Find:

Which of the boat returns to the starting point first

Solution:

Let the total time taken by Boat A and Boat B be ta and tb respectively.

For Boat A:

Net velocity while moving upstream = Velocity of boat in still water - Velocity of river flow

= 10-5 km/hr = 5km/hr

Time for the upstream journey = 1 / 5 hr

Net velocity while moving downstream = Velocity of boat in still water + Velocity of river flow

= 15km/hr

Time for the downstream journey = 1/ 15 hr

ta = 1/5 + 1/15 = 4 / 15 hr ≈ 0.266 hr

For Boat B:

Velocity during the journey = Resultant vector velocity of boat and river

= $\sqrt{5^2 + 10^2}$

= $\sqrt{125}$

Time = 1 /  $\sqrt{125}$

tb= 2 /  $\sqrt{125}$ ≈ 0.178 hr

Since tb < ta, the second boat returns to the starting point first.