Question

1.
A boat crosses a river of width 200 m in shortest
time and is found to experience a drift of 100 min
reaching the opposite bank. The time taken now is
t. If the same boat is to cross river by shortest path,
the time taken to cross will be
(1) 21
(2) √2
(3) 3t
(4)2t/√3​

Answer 1

Answer:

1 is the right and correct answer

Answer 2

The time taken to cross will be: 4) 2t/√3​.

Given:

A boat crosses a river of width 200 m

Experience a drift of 100 min

To find:

The time taken to cross.

Solution:

Velocity of boat = 200/t. (Vₐ)

Due to drift, velocity = 100/t (Vₐ)

Vᵣ = Vₐsinθ

100/t =  200/t sinθ

From this, sinθ = 100/200

sinθ = 1/2 which means θ = 30°.

The horizontal component of the boat's velocity while crossing the river by the shortest path is Vₐ.

V = Vₐ cos30∘

Let tₐ be the time taken to cross river

Substituting the value of V in the initial velocity of boat equation:

Vₐ cos30∘ = 200/tₐ.

Here this also becomes 200/t cos30∘ = 200/tₐ.

Solving, this we obtain tₐ = 2t/√3.

Therefore, the time taken to cross the river by shortest path is 2t/√3​.

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