Taylor decides to search for hard evidence to support his "they never landed on the moon theory" so he gets into his cactus powered mobile and drives. he begins by driving 50.0km [N]. he then turns and drives 30.0k [N30E]. he comes to his futile search by driving 25.0 km [w] and then 40.0 km [sw]. if Taylors entire trip took 8.5 hours, find his average velocity.
his displacement that I got was 61 km and his average speed was 4.7m/s. if you needed to know
I translated all to vectors:
50.0km [N] ---> 50(cos90,sin90) = (0,50)
30.0k [N30E] ---> 30(cos60,sin60) = (15,25.9808)
25.0 km [w] --> 25(cos180,sin180) = (-25, 0)
40.0 km [sw] --- 40(cos225,sin225) = (-28.28427, -28.28427)
resultant vector = (-38.28427, 47.69653)
magnitude = √((-38.28427)^2 + 47.69653^2) = 61.16 km
velocity = distance/time = 61.16 km/8.5 hrs = 7.195 km/h or appr 7.2 km/h
the sum of his displacement vectors is
<0,50> + <30*0.5,30*0.866> + <-25,0> - <40*0.707 + 40*0.707> = <-38.28,47.7>
So your final displacement and speed have the right magnitude, but we are dealing with vectors here. The average velocity is
4.7 m/s (16.92 km/hr) in the direction N 38.75° W
oops. I did not check your division to verify the speed.
To find Taylor's average velocity, we need to divide his displacement by the total time taken. Displacement is the straight-line distance from the starting point to the ending point.
In this case, we already have the displacement as 61 km. Now, let's calculate the total time taken:
- Taylor drove 50.0 km [N] at some speed. We don't know the time taken or his speed for this leg of the trip, so we can't calculate it.
- Taylor then drove 30.0 km [N30E]. Again, we don't know the time taken or his speed for this leg of the trip.
- Taylor drove 25.0 km [W]. We don't know the time taken for this leg, but we need to convert the distance from kilometers to hours. Assuming Taylor drove at a constant speed throughout, we divide the distance by his speed. Let's say he traveled at x km/h: 25.0 km = x km/h * t hours, where t is the time taken. We can rearrange this equation to get t = 25.0 km / x km/h.
- Taylor finally drove 40.0 km [SW]. Similar to the previous leg, we divide the distance by the speed to get the time taken: t = 40.0 km / x km/h.
The total time taken is the sum of the time taken for each leg: 8.5 hours = t1 (unknown) + t2 (unknown) + t3 (25.0 km / x km/h) + t4 (40.0 km / x km/h).
We don't have enough information to determine the average velocity since we don't know the time or speed for the first two legs of the trip.