A hunter wishes to cross a river that is 1.6 km wide and that flows with a speed of 4.8 km/h. The hunter uses a small powerboat that moves at a maximum speed of 9.6 km/h with respect to the water. What is the minimum time necessary for crossing?
minimum time,head straight across.
timeacross= 1.6km/4.8km/hr=1/3 hr
To find the minimum time necessary for crossing, we need to consider the relative velocity of the boat with respect to the shore.
First, let's find the time it would take for the boat to cross the river without any current. We can use the formula:
Time = Distance / Speed
The distance to be covered is the width of the river, which is 1.6 km. The speed of the boat is its maximum speed of 9.6 km/h. Therefore, the time it would take to cross the river without any current is:
Time = 1.6 km / 9.6 km/h = 0.1667 hours
Now, let's consider the effect of the river current. Since the current flows perpendicular to the motion of the boat, it will affect the boat's velocity and the direction in which it travels.
To analyze the effect of the current, we need to use vector addition. The velocity of the boat in still water is 9.6 km/h, and the speed of the river current is 4.8 km/h. Since both velocities are in the same direction (across the river), we can simply add them:
Boat Velocity = Boat Speed + River Current Speed = 9.6 km/h + 4.8 km/h = 14.4 km/h
Next, we need to find the time it would take for the boat to cross the river with the combined velocity of the boat and the current. We can again use the formula:
Time = Distance / Speed
The distance to be covered is still 1.6 km, but the speed of the boat is now 14.4 km/h. Therefore, the time it would take to cross the river with the current is:
Time = 1.6 km / 14.4 km/h = 0.1111 hours
Therefore, the minimum time necessary for crossing the river is 0.1111 hours, or approximately 6.67 minutes.