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
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
See the answer below...
Explanation:
Velocity is
#120"km"//"h"# . We also know,#s=vt" ";# s#=# displacement#" ";v=# velocity#" ";t=# time
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....
