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# Vectors

1) A river 35 m wide flows south at a speed if 15 m/s. What must be the velocity and heading of the boat if it is to move directly from the west bank to the east bank in 5 seconds?

2) Two tractors are hooked to a combine. the combine needs to be pulled due east at 400 N. One tractor is pulling at 190 N, 32degrees S of east. What angle and force must the second tractor be doing?

#### Solution Preview

1) A river 35 m wide flows south at a speed if 15 m/s. What must be the velocity and heading of the boat if it is to move directly from the west bank to the east bank in 5 seconds?

Distance = 35 m
Time = 5 s
Therefore resultant velocity = Distance / Time = 35/5= 7 m/s

Component is the horizontal (x) direction = (Magnitude) x (Cos phi )
Component is the vertical (y) direction = (Magnitude) x (Sin phi )

Let East direction be the positive x axis and North the positive y axis

Velocity of river = 15 m/s S of East
S of East mean an angle of - 90 degrees

Magnitude = 15 m/s
phi = -90 degrees ...

#### Solution Summary

Calculates the velocity and force.

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