An object is released at one bank of river flowing with speed 5km/h towards east.air is blowing with speed 5km/north.if width of river is 200m ,then time taken by floating object to reach the other banks is?

Question

Answer

Solution:

Understanding the problem:

An object is released at one bank of river flowing with speed 5km/h towards east. Air is blowing with speed 5km/north. If the width of the river is 200m, then time taken by floating object to reach the other banks is?

Solving the problem:

To solve this problem, we need to use the concept of relative velocity. The velocity of the object with respect to the ground is the vector sum of its velocity with respect to the water and the velocity of the water with respect to the ground.

Horizontal motion:

The object is moving towards the east bank of the river. Therefore, its velocity with respect to the water is also towards the east bank.

Let v_o/w be the velocity of the object with respect to the water.

v_o/w = 0 km/h (since the object is floating on the water)

The velocity of the water with respect to the ground is also towards the east bank.

Let v_w/g be the velocity of the water with respect to the ground.

v_w/g = 5 km/h towards east (given)

Therefore, the velocity of the object with respect to the ground is:

v_o/g = v_o/w + v_w/g = 0 + 5 = 5 km/h towards east

Vertical motion:

The air is blowing towards the north. Therefore, its velocity with respect to the ground is towards the north.

Let v_a/g be the velocity of the air with respect to the ground.

v_a/g = 5 km/h towards north (given)

Resultant velocity:

The velocity of the object with respect to the ground is towards the east and the velocity of the air with respect to the ground is towards the north. Therefore, the resultant velocity of the object with respect to the ground is the vector sum of its velocity towards the east and the velocity towards the north.

Let v_o/g,a/g be the resultant velocity of the object and the air with respect to the ground.

v_o/g,a/g = √(v_o/g² + v_a/g²) = √(5² + 5²) = √50 ≈ 7.07 km/h

Time taken to cross the river:

Let t be the time taken by the object to cross the river.

The distance to be covered by

Answer

Ans is 102 seconds

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