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
My pc...
As per image the angle is
color(red)(theta wheretheta=tan^(-1)(3/4)
Hence,costheta=4/5" ";" "sintheta=3/5
- The effective velocity on the
x axis(i) is120 cdot costheta=120xx4/5=96"km"//"h" - The effective velocity on the
y axis(j) is120 cdot sintheta=120xx3/5=72"km"//"h" Now, The distance covered on the
x axis is96t" " unit and ony axis is72t" " unit.In
i,j,k form ,the answer iscolor(red)(96thati-72thatj Hope it helps...
Thank you....