A particle experiences a constant acceleration that is north at 100 m/s^2. At t=0, its velocity vector is 60 m/s east. At what time will the magnitude of the velocity be 100 m/s?

Question

A particle experiences a constant acceleration that is north at 100 m/s^2.  At t=0, its velocity vector is 60 m/s east.  At what time will the magnitude of the velocity be 100 m/s?

drwls · Answer

The eastward component will remain 60 m/s at it acquires a northward component.

Thinking of a 3,4,5 right triangle, you should be able to see that the velocity magnitude (the hypotenuse of the vector velocity triangle) will be 100 m/s when the northward velocity component is 80 m/s.

The particle will achieve that velocity
when 100 m/s^2*t = 80 m/s
which is t = 0.8 s.