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Addition vector of two velocities

When a truck creeps along in traffic at a speed of 5 m/s, a man walks diagonally across the back of the truck at 3m/s. To a traffic helicopter in a stationary position above the road the road, the man's apparent motion is the superposition of these two motions; that is, his apparent velocity is the vector sum of the two given velocities. If the directions are shown as below, find the magnitude and direction.

velocity man of truck = 3m/s (angle is 40 dg)
velocity on road = 5 m/s (angle is 15 degrees)

Solution Preview

I want to set up these in a x,y or i, j orthonoraml coordinate system

I am assuming the angle from the i direction vector is given in the above description:
v man vector = 3 m/sec cos(40) i + 3 m/sec sin(40) j
Vtruck vector = 5m/sec cos(15) i+ 5 m/sec sin(15) j

Vtotal vector =
{3 m/sec cos(40) +5m/sec cos(15)} i + {3 m/sec sin(40) + 5 m/sec sin(15)}j

7.127762461 i + 3.222458055 ...

Solution Summary

This solution is provided in 363 words. It uses a coordinate system and vector calculations to show the answer, and also provides another example of working with a vector problem.