A boat travels up stream in a river with a constant but unknown speed V with respect to water. At the start of this trip upstream, a bottle is dropped over the side. After 7.5 minutes the boat turns around and heads downstream. It catches up the bottle when the bottle has driffted 1 km down stream from the point at which it was dropped into water. Then the velocity of water current is?
2007-01-17 22:52:54 · 1 answers · asked by Ekant 2 in Science & Mathematics ➔ Physics
The velocity of water is 4 km/h.
The trick is to understand that 7.5 minutes is the half-way trip. Because the speed of the boat relative to the bottle is constant = V. So if the boat drops the bottle, then travel upstream for 7.5 minute, then returns, the return trip is necessarily equal in duration to the upstream trip: 7.5 minute. So the bottle will have traveled 1 km in 15 minutes, thus 4 km/h.
You can verify that for any speed of the boat this works.
If speed of boat is 60 km/h
Distance traveled upstream = (60-4)*7.5/60 = 7km
Distance traveled dnstream = (60+4)*7.5/60 = 8km
If speed is 973 km/h
Distance traveled upstream = (973-4)*7.5/60 = 121.125 km
Distance traveled dnstream = (973+4)*7.5/60 = 122.125 km
As you can see the difference is always 1km: the distance traveled by the bottle.
2007-01-18 00:58:04 · answer #1 · answered by catarthur 6 · 1⤊ 0⤋