SOLUTION: Cathy rows a boat directly across a river at a constant x-velocity. The river is 200 m wide and it takes Cathy 62.5 seconds to cross the river. When she reaches the other side, Cat
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-> SOLUTION: Cathy rows a boat directly across a river at a constant x-velocity. The river is 200 m wide and it takes Cathy 62.5 seconds to cross the river. When she reaches the other side, Cat
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Question 1164942: Cathy rows a boat directly across a river at a constant x-velocity. The river is 200 m wide and it takes Cathy 62.5 seconds to cross the river. When she reaches the other side, Cathy has floated 750 m downstream (Dy)
a) What is the horizontal velocity (vx) of Cathy's boat as she crosses the river? answer is 3.2m/s
b) how fast is the river flowing : answer 12m/s
c) what is cathy's total velocity : answer 12.42m/s at 75.1 below x axis
d) how long would it take cathy to cross the river if there was no current
can you pls show the approach and solve the questions. i gave the range the answers are suppsoed to be in. thanks! Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the way i see this problem is that the river is vertically oriented.
the direct path of the boat across the river is horizontal.
the vertical drift of the boat is equal to the rate of the river.
the time to get across the river is 62.5 seconds.
in that 62.5 seconds, the boat has traveled 200 meters in a horizontal direction.
that puts its speed directly across the river at 200 / 62.5 = 3.2 meters per second.
in that same 62.5 seconds, the boat has traveled 750 meters downstream in a vertical direction.
that puts its speed directly vertical down the river at 750 / 62.5 = 12 meters pet second.
her total velocity is the hypotenuse of the right triangle formed.
that distance is sqrt(200^2 + 750^2) = 776.2087348 meters.
the average speed for the direction the boat travels is that divided by 62.5 = 12.41933976 meters per second.
the horizontal speed is the speed of the boat without any current.
that means it would take the boat 3.2 seconds to cross the river without any current causing it to travel downstream as well.
the vertical speed is the speed of the current.
that's because nothing is causing the boat to go downstream except the speed of the current.
without the current, the angle the boat takes to get across the river is 0 degrees from the horizontal.
with the current, the angle the boat takes to get across the river is 75.1 degrees from the horizontal.
that's because the river is pushing the boat down at a greater rate than the boat's motor is pushing it across.
here's my worksheet.
note that speed is distance traveled divided by time and velocity is displacement divided by time.
this means that the speed in the horizontal direction is the horizontal velocity because it's the displacement in the horizontal direction divided by the time.
likewise, this means that the speed in the vertical direction is the vertical velocity because it's the displacement in the vertical direction divided by the time.
the direct direction is the straight line path from the point of origin to the destination.
that's the hypotenuse of the triangle formed.
the speed in that direction is the direct velocity.
here's a reference on velocity you might find helpful.
don't forget to answer the questions at the end of the tutorial.
they're informative as well.
