A boat is heading directly North acroos a river at 5km\h. The river is flowing east at 3km\h.
a) what is the actual velocity of the boat?
b) how far down stream does it land if the trip takes 0.5 hrs.
c) how wide is the river?
a. V = 3 + 5i = 5.83km/h[59o].
b. d = 3km/h * 0.5h = 1.5 km.
c. Width = 5km/h * 0.5h = 2.5 km.
To answer these questions, we need to break down the velocity of the boat into its components: one in the north direction and the other in the east direction.
a) To find the actual velocity of the boat, we can use the Pythagorean theorem. The north velocity is 5 km/h, and the east velocity is 3 km/h (the velocity of the river). Therefore, the actual velocity is given by:
Actual velocity = √((north velocity)^2 + (east velocity)^2)
Actual velocity = √((5 km/h)^2 + (3 km/h)^2)
Actual velocity = √(25 km^2/h^2 + 9 km^2/h^2)
Actual velocity = √(34 km^2/h^2)
Actual velocity ≈ 5.83 km/h
Therefore, the actual velocity of the boat is approximately 5.83 km/h.
b) To find how far downstream the boat lands, we need to calculate the displacement in the east direction. The time taken for the trip is 0.5 hours, and the east velocity is 3 km/h. Using the equation:
Displacement = velocity x time
Displacement = 3 km/h x 0.5 h
Displacement = 1.5 km
Therefore, the boat lands 1.5 km downstream.
c) To find the width of the river, we can calculate the displacement in the north direction. Since the boat is moving directly north, the displacement in the north direction will be equal to the north velocity multiplied by the time:
Displacement = 5 km/h x 0.5 h
Displacement = 2.5 km
Therefore, the width of the river is 2.5 km.