A bus drives 40.0 km [E] from town A to town B, then another 30.0 km [S] to town C in a total time of 1.00 h. What are the values of its average speed and average velocity, respectively?
a) 70.0 km/h, 70.0 km/h [37º S of E]
b) 50.0 km/h, 70.0 km/h [37º S of E]
c) 50.0 km/h, 50.0 km/h [37º S of E]
d) 70.0 km/h, 50.0 km/h [37º S of E]
e) 50.0 km/h [37º S of E], 70.0 km/h
To find the average speed, we divide the total distance traveled by the total time taken. The total distance traveled is the sum of the distances from A to B and from B to C, which is 40.0 km + 30.0 km = 70.0 km. The total time taken is 1.00 h. Therefore, the average speed is 70.0 km/h.
To find the average velocity, we need to consider both the displacement and the time taken. The displacement is the straight-line distance from A to C, which is 40.0 km [E] (east) and 30.0 km [S] (south), so the displacement is the vector sum of these two displacements, which can be found using the Pythagorean theorem.
The magnitude of the displacement is √(40.0^2 + 30.0^2) = √(1600 + 900) = √2500 = 50.0 km. The direction of the displacement can be found using trigonometry:
tan(θ) = opposite/adjacent = 30.0 km / 40.0 km = 0.75
θ = arctan(0.75) = 37º
Therefore, the average velocity is 50.0 km/h [37º S of E].
So, the answer is option d) 70.0 km/h, 50.0 km/h [37º S of E].