Exams › JEE Advanced › Physics

A swimmer can cross a still river of width d to a point exactly opposite the starting bank in time t0. When the river has a current, the swimmer still manages to reach the directly opposite point (same path), but now takes time t1 > t0. What is the speed of the river current?

1. d / sqrt(t1 * t0)
2. d * sqrt(t1² - t0²) / (t1 * t0)
3. d / sqrt(t1² - t0²)
4. d * sqrt(t1² + t0²) / (t1 * t0)

Correct answer: d * sqrt(t1² - t0²) / (t1 * t0)

Solution

The swimmer's speed in still water is vₛ = d/t0. With a current v_w, to go straight across the swimmer angles upstream so resultant perpendicular speed = sqrt(vₛ² - v_w²) = d/t1. Solving for v_w gives d*sqrt(t1² - t0²)/(t0*t1).

Related JEE Advanced Physics questions

• A person riding in a hot-air balloon experiences an upward acceleration of 4.9 m/s². Exactly 2 seconds after the balloon is released from ground level, the person drops a small object. Taking g = 9.8 m/s², find the maximum height above the ground that the dropped object reaches.
• An object is released from rest at some height above the ground. In addition to gravity, air exerts a constant horizontal acceleration on the object throughout its fall. The path of the object as seen from the ground frame will be a
• A car can produce a maximum acceleration of 5 m/s² and its brakes can produce a maximum retardation of 10 m/s². Assuming the car starts from rest and must come to rest at a destination 1500 m away, find the minimum time (in seconds) to travel this distance.
• From the top of a 100 m tower, a particle is thrown vertically upward with speed 50 m/s at t = 0. Two seconds later, a second particle is projected vertically upward from the ground with the same speed 50 m/s. At what time after t = 0 are the two particles at the same height?
• The velocity of a particle traveling in a straight line is given by v(t) = 5 - 6*e^(-t/2) m/s, where time t is in seconds and t >= 0. At t = 0, the particle is at position x = 7 m. The position as a function of time is x(t) = k*t + l*e^(-t/2) + m. Find the numerical value of (k + m) / l.
• A spy is standing on a bridge above a road. He notices a flatbed truck approaching at 30 m/s. He knows the telephone poles along the road are spaced 20 m apart. The bed of the truck is 20 m below the bridge. He needs to calculate how many poles away the truck should be when he jumps off the bridge so that he lands on the truck. How many poles away is the truck when he should jump? (Take g = 10 m/s²)

⚔️ Practice JEE Advanced Physics free + battle 1v1 →