A hunter wishes to cross a river that is 1.17 km
wide and flows with a speed of 1 km/h parallel to its banks. The hunter uses a small
powerboat that moves at a maximum speed
of 15 km/h with respect to the water.
What is the minimum time necessary for
crossing?
Answer in units of min
Thank you!
TanA = (1km/h)/15km/h = 0.066666
A = 3.8o E. of N.
d = 1.17/cos3.8 = 1.173km. = Distance
boat must travel.
Vb = 15/cos3.8 = 15.033 km/h
d = V*t = 1.173 km
15.033t = 1.173
t = 0.078028 h = 4.68 Min.
To find the minimum time necessary for crossing the river, we need to consider the speed of the boat and the speed of the river.
Let's assume the hunter is trying to cross the river directly, from one bank to the other.
Since the river is flowing parallel to its banks, the velocity of the river will not affect the distance the boat needs to travel (1.17 km), but it will affect the time it takes to cross.
We can break down the boat's velocity into two components: one parallel to the river (which is the maximum speed of 15 km/h), and one perpendicular to the river (due to the current of the river).
Since the river is flowing with a speed of 1 km/h parallel to the banks, the boat's velocity perpendicular to the river is 0 km/h (since the boat is not moving sideways relative to the river).
To find the time it takes to cross the river, we can divide the distance by the boat's velocity:
Time = Distance / Velocity
Time = 1.17 km / 15 km/h
Now, we can calculate the time it takes to cross the river:
Time = 0.078 min
Therefore, the minimum time necessary for crossing the river is approximately 0.078 minutes or 4.7 seconds.