I was asked to state as a product of speed and unit vector a mass traveling at 1000ft/sec along the vector <1,sqrt(3)>. I know that v/|v| gives me the unit vector, which is (1/2i, sqrt(3)/2j). Do I keep the speed as given?
"product"? What does that mean in vectors?
I suspect the problem means NOT the product, but to indicate the velocity as a vector. IF so, then speed along the direction of the vector is 1000, but looking at the triangle (1,sqr3, 2) then
velocity=1000*cosTheta *i + 1000*sinTheta*j
= 500 i +866 j
Opps
velocty=500i +.573 j
Most probably I misunderstood the question and quite frankly I thought this might be the answer, but in the answer box it did ask for the unit vector and the speed, which confused me. (This is a problem that I have already answered rightly or wrongly).
To find the product of speed and unit vector, you need to multiply the speed (magnitude of velocity) with the unit vector.
In this case, you correctly found the unit vector of the given velocity vector, which is (<1/2, sqrt(3)/2>).
Now, to complete the answer, you need to multiply the unit vector by the speed. The speed given is 1000 ft/sec.
To do this calculation, you simply multiply each component of the unit vector by the speed:
(<1/2, sqrt(3)/2>) x 1000 ft/sec.
Multiplying each component of the unit vector by the speed, we get:
(<1/2 x 1000 ft/sec, sqrt(3)/2 x 1000 ft/sec>) = (<500 ft/sec, 500√3 ft/sec>).
So, the product of speed and unit vector for a mass traveling at 1000 ft/sec along the vector <1, sqrt(3)> is <500 ft/sec, 500√3 ft/sec>.