A small boat is crossing a river which flows at 10km.h. The driver of the boat keeps it heading directly (at 90) away from the bank at a speed of 24 km/h relative to the water. The river is 0.5 km wide.
I calculated the speed of the boat relative to land - 26km/h
I calculated the direction the boat is actually traveling - 67* from bank
I calculated the time to get to the opposite bank - 1.25min
How far downstream will the boat drift before reaching the opposite bank?
How do I calculate that. ^
Yes, 5, 12 13 is a right triangle like 345 so you know without your calculator that 10^2 + 24^2 = 26^2
tan A = 10/24
so
A = 22.6 from straight across so 67.4 from the bank
time = .5/24 = .02083 hr = 1.25 min.
speed downstream = 10 km/hr
time under way = .02083 hr
distance = .2083 km
Can you help me with this question, too?
Suppose that the boat is supposed to arrive at a point directly across the river from its starting point.
a) What should be the heading of the boat?
To calculate how far downstream the boat will drift before reaching the opposite bank, you can use the concept of relative velocity.
The boat is moving at a speed of 24 km/h relative to the water, while the river is flowing at a speed of 10 km/h. Therefore, the effective speed of the boat relative to the land is 24 km/h + 10 km/h = 34 km/h. This is the speed the boat is actually moving in relation to the bank.
Since the boat is moving directly away from the bank, the angle between the boat's heading and the river flow is 90 degrees. This means that the boat's velocity vectors are perpendicular to each other.
Now, let's consider the situation when the boat reaches the opposite bank. During this time, the boat has traveled a distance equal to the width of the river, which is 0.5 km. To find the time it takes for the boat to cross the river, we can divide this distance by the effective speed of the boat relative to the land:
Time = Distance / Speed
Time = 0.5 km / 34 km/h
Time ≈ 0.0147 hours
Now, we know that the boat drifts downstream during this time. To calculate the distance downstream, we multiply the time it takes to cross the river by the speed of the river:
Distance Downstream = Time × Speed of the River
Distance Downstream = 0.0147 hours × 10 km/h
Distance Downstream ≈ 0.147 km or 147 meters
Therefore, the boat will drift approximately 147 meters downstream before reaching the opposite bank.