Finding velocity when given magnitude and direction?

Given that i= eastward and j=northward: At noon Q is at O and at time t hours after noon the position vector of Q is q km. The velocity of Q has magnitude 120 km/h in the direction of (4i – 3j). Find an expression for q in terms of t? (The answer is 96ti-72tj)

The part that I'm struggling with is finding an expression for the velocity. I don't understand how to combine the magnitude and direction to give the velocity

1 Answer
Feb 3, 2018

See the answer below...

Explanation:

Velocity is 120"km"//"h". We also know, s=vt" ";s= displacement" ";v=velocity" ";t=time
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As per image the angle is color(red)(theta where theta=tan^(-1)(3/4)
Hence, costheta=4/5" ";" "sintheta=3/5

  • The effective velocity on the x axis(i) is 120 cdot costheta=120xx4/5=96"km"//"h"
  • The effective velocity on the y axis(j) is 120 cdot sintheta=120xx3/5=72"km"//"h"

Now, The distance covered on the x axis is 96t" "unit and on y axis is 72t" "unit.

In i,j,k form ,the answer is color(red)(96thati-72thatj

Hope it helps...
Thank you....