A hunter wishes to cross a river that is 1.6 km wide and flows with a speed of 5.0 km/h parallel to its banks. The hunter uses a small powerboat that moves at the maximum speed of 11 km/h with respect to the water . What is the minimum time necessary for crossing ?
Min time will be to head directly across the river, but that puts him downstream due to river current. Now if he wanted to land directly across the river, that is another question.
To find the minimum time necessary for crossing the river, we need to determine the angle at which the hunter should point the boat in order to minimize the time.
Here's how we can approach this problem:
1. First, let's find the velocity of the boat with respect to the ground. Since the river is flowing parallel to its banks, the velocity of the river will not affect the time taken to cross. Therefore, the velocity of the boat with respect to the ground is the vector sum of its velocity with respect to the water and the velocity of the river.
Boat's velocity with respect to ground = Boat's velocity with respect to water + Velocity of the river
The velocity of the river is given as 5.0 km/h (because it flows parallel to its banks), and the boat's maximum speed with respect to the water is 11 km/h (given in the question). Therefore, the boat's velocity with respect to the ground is:
Boat's velocity with respect to ground = 11 km/h + 5.0 km/h = 16 km/h
2. Now, let's determine the time it would take for the boat to cross the river. We can use the formula:
Time = Distance / Velocity
The distance to cross the river is given as 1.6 km, and the velocity of the boat with respect to the ground is 16 km/h (which we found in step 1). Therefore, the time required to cross the river is:
Time = 1.6 km / 16 km/h = 0.1 h = 6 minutes
So, the minimum time necessary for crossing the river is 6 minutes.