Solving Motorist's 7min Trip Vectors & Speeds

[chocolatelover]

Homework Statement

A motorist drives south at 24.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 3.00 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 7.00 min trip, find the following values.
a. Total vector displacement displacement
b. Average speed
c. average velocity

Homework Equations

The Attempt at a Solution

a. Δr=24m/s(180s)south+25m/s(180s)west+30m/s(60s)north west

=4320m(-j)+4500m(-i)+1272.8(-i)+1272.8j Would this "j" be positive or negative?
=-5772.8i-3047.208

square root ((-5772.8)^2+(-3047.208)^2)=6527.680

θ=tan-1(3047.208/5772.8) or would it be tan-1(3047.208/5772.8)
=27

b. average speed=4320+4500+1800
1062/7(1/60)=
25.286

c. Would the average velocity direction be the same as the one from part a?

Thank you very much

 

[luben]

a. yes you got it correct. that j should be positive since he is going north at that moment.
b. the average speed is also correct. another quicker way to get it is a weighted mean of the 3 speed.
c. yes the direction should be that of a. it means the total displacement per over total time.

 

[chocolatelover]

Thank you very much

Regards