Read Question Below!

Question

A bus driver heads south with a steady speed of v₁ = 20.0 m/s for t₁ = 3.00 min, then makes a right turn and travels at v₂ = 25.0 m/s for t₂ = 3.00 min, and then drives northwest at v₃= 30.0 m/s for t₃ = 1.00 min. For this 7.00-min trip, calculate the following. Assume +x is in the eastward direction.

(a) total vector displacement (Enter the magnitude in m and the direction in degrees south of west.)

magnitude: _______m

direction: _______ ° south of west_

(b) average speed (in m/s): ______m/s

(c) average velocity (Enter the magnitude in m/s and the direction in degrees south of west.)

magnitude: ______m/s

direction: _______° south of west

Answer 1

103.737 m

23.96 degrees south of west

average speed = total distance traveled divided by 7 = (60+75+30)/7 165/7 = 23. 4/7 mph

average velocity = the displacement/7 = 103.737/7 = 14.820 m/s 23.96 degrees south of west

It helps to draw a diagram. If he's going south and then makes a right, he's then going west

the driver went 60 m south, then 75 west, then 30 northwest. That's a total mileage of 165 m in 7 minutes, an average speed of 165/7 = 23.571 m per minute or 7 4/7 m per min.'

draw the displacement on a diagram, connect the starting point to the finishing point

calculate that distance. it's the hypotenuse of a right triangle with sides 60-15sqr2 and 75+15sq2

Use the distance formula, h^2 = (60-15sqr2)^2 + (75+15sqr2)^2 h=103.737 approximately.

or h^2 = 96.213^ + 38.787^2 expand, solve for h = the displacement, = distance from start to finish as the crow flies.