Susan, driving north at 60 mph, and Trent, driving east at 45 mph, are approaching an intersection. What is Trent’s speed relative to Susan’s reference frame?

So Trent is moving at 75mph 53.13° Southwest of Susan.

Explanation:

Given

Susan moves south direction at 60mph

Trent moves east direction at 45 mph

Trent relative velocity can be obtained using the polar coordinate

So converting these cartessian system to polar coordinate using the formula

R=✓(y^2+x^2)

and it's angle by arctan(y/x)

R=√(60^2+45^2)=√(5625)=75mph

Direction=arctan (-60/45)=-53.13°

Assume north direction is positive axis and south Negative direction

So Trent is moving at 75mph 53.13° Southwest of Susan.

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