A motor boat going down stream ,overtakes a floating object in water .One hour later,the motor boat turned back .If speed of motor boat in still water is constant and flow velocity is also assumed constant,motor boat will again pass the floating object after time t given by 1)Greater than 2 hrs 2)Equal to 2 hrs 3)less than 2 hrs 4)less than 1 hr

To solve this problem, we need to analyze the motion of both the motorboat and the floating object in the water. Let's break it down step by step.

Understanding the Scenario

We have a motorboat moving downstream, which means it is aided by the current of the water. The boat overtakes a floating object, which we can assume is stationary relative to the water. After one hour of traveling downstream, the motorboat turns around and heads back upstream.

Key Variables

• Speed of the motorboat in still water: Let's denote this as Vb.
• Speed of the current: We'll denote this as Vc.
• Effective speed downstream: This is Vb + Vc.
• Effective speed upstream: This is Vb - Vc.

Calculating Distances

When the motorboat travels downstream for one hour, it covers a distance of:

D = (Vb + Vc) * 1

After this hour, the motorboat turns around. At this point, the floating object has also been drifting downstream for one hour, covering a distance of:

D_f = Vc * 1

Distance Between the Boat and the Object

When the boat turns back, the distance between the motorboat and the floating object is:

Distance = D - D_f = (Vb + Vc) - Vc = Vb

This means that when the motorboat turns around, it is Vb distance away from the floating object.

Time to Catch Up

Now, the motorboat is traveling upstream at a speed of Vb - Vc. To find the time t it takes for the motorboat to catch up to the floating object, we can use the formula:

Time = Distance / Speed

Substituting the values we have:

t = Vb / (Vb - Vc)

Analyzing the Time

Now, we need to determine how this time compares to 2 hours. We can analyze the fraction:

t = Vb / (Vb - Vc)

As Vc (the speed of the current) increases, the denominator decreases, making t larger. Conversely, if Vc is small compared to Vb, t will be closer to 1 hour. However, since the boat has to cover the distance Vb while moving against the current, it will take more than 1 hour but less than 2 hours to catch up to the floating object.

Final Conclusion

Thus, the motorboat will pass the floating object again after a time t that is:

Less than 2 hours.

In summary, the answer to the question is that the motorboat will again pass the floating object after a time that is less than 2 hours. This is due to the relative speeds of the boat and the current, which affect how quickly the boat can return to the floating object.