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
My pc...

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....