You enter an antique classic car road rally with your 1956 Studebaker Golden Hawk. The rally course consists of the following segments: travel north at 21.0 m/s for 30.0 min, then east at 32.0 m/s for 40.0 min, and finally northeast at 35.0 m/s for 50.0 min. For the entire trip, determine the following.
(a) displacement vector (magnitude and direction) and distance traveled displacement vector magnitude displacement vector direction distance North of East
(b) average velocity vector (magnitude and direction) and average speed average velocity vector magnitude average velocity vector direction average speed m/s North of East

The answers to the question are

(a) The displacement vector is 146246.212 i + 146246.212 j

Magnitude of the displacement = 151052.536 m

Displacement direction is   37.46 ° North of East.

(b) The average velocity is

= 27.08 i + 23.343 j

The magnitude of the average velocity is 35.75 m/s

The direction of average velocity is 49.239 ° North of East.

Explanation:

We note the displacement and the direction for each of the stage as follows

Travel direction      Travel velocity    Duration         Displacement

North                        21.0 m/s              30.0 min        37800 m

East                          30.0 m/s             40.0 min         72000 m

North east                35.0 m/s             50.0 min         105000 m

We note that the total distance moved north is given by

37800 + 105000×sin(45) = 37800 m + 74246.2 m = 112046.212 m

The total distance moved east is given by

72000 m + 74246.2 m = 146246.212 m

The displacement vector is given as

Δr = r₂ - r₁ = (x₂ - x₁)i + (y₂ - y₁)j + (z₂ - z₁)k

= 146246.212 i + 146246.212 j

Therefore the magnitude of the displacement is given by

= 151052.536 m

The direction is given by tan⁻¹ =  37.46 ° North of East

(b) The average velocity vector is given by knowing the displacement vector thus

Displacement vector =Δr = r₂ - r₁ = (x₂ - x₁)i + (y₂ - y₁)j + (z₂ - z₁)k

and   that is vₐ = Δr/Δt

Therefore if we take our east to be the x axis, and the north to be our y axis, we have

Total displacement east is given above as 146246.212 m

Time taken to move east = 40+50 = 90 min = 5400 s

Average velocity in the x direction = 27.08 m/s

Total displacement North is given above as 112046.212 m

Time taken to move east = 30+50 = 80 min = 4800 s

Average velocity in the x direction = 23.343 m/s

The average velocity therefore is

v(average) = 27.08 i + 23.343 j

Magnitude of the average velocity = 35.75 m/s

The direction of average velocity is given by tan⁻¹ = 49.239 ° North of East.

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.

i think the answer would be reserve.