Question

12 fect, and forward (along the takes 4o lef to right on a highway. The standard width of a highway lane is recton and th) a a contant 65 mph the entire time. The lane change is taking place in di y direction) at a constant 65 mph the entire time, stant speed in that direction as it changes lanes, velociy vector, measured in mph (miles/hour)? Remem a) What is the x there are $280 feet m me te S2s00d.oo 4s- o.ooll hr b) What is the instantancou s speed (magnitude of the velocity vector) of the car while changing lanes? c) What angle will the car's path make with the y-axis? (This is the smaller of the two angles you might be considering. Draw a picture if you're not sure.) Your answer to (b) explains why you don't really have to speed up in order to change lanes, and your answer to (c) explains why you barely have to move the steering wheel at all!

dont understand

Answer 1

part a:

x component of car's velocity vector=distance to be covered along x axis/time taken

=12 feet/(4 seconds)

=3 ft/s

in mph, answer=3*3600 ft/hr=2.0455 mph

part b:

instantaneous speed=sqrt(velocity along x^2+velocity along y^2)

=sqrt(65^2+2.0455^2)

=65.032 mph

part c:

angle with y axis=arctan(x component/y component)

=1.8025 degrees