# 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?

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#### 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

The expert calculates the velocity and force. The velocity and heading of the boat if it is to move directly from the west bank to the east bank in five seconds is determined.