Assume all speeds are constant. a) A man walks up a stalled escalator in time tw

Question

Assume all speeds are constant.

a) A man walks up a stalled escalator in time tw = 92 s. If he stands on the moving escalator, he reaches to top in time tm = 27.2 s. Find twm, the time it would take him to reach the top if he walked up the moving escalator?
t = s

b) A plane flies at speed vstill = 244 km/h in still air. Now, there is a wind blowing at speed vw = 64.7 km/h, with its direction at 47 degrees to the east of north. If the pilot wishes to fly due north with the wind blowing, find:
- the angle between the direction the plane flies and due north: ? = degrees
- the speed at which the plane will fly relative to the ground: vp = km/h

Explanation / Answer

a) let distance be x
then speed in stalled sw=x/92
in moving sm=x/27.2
now speed will add then time=x/(x/92+x/27.2)=20.99 sec
b)vstill= 244 km/h
vw=64.7km/h at 47 degree
component of wind in east direction=64.7*sin47=47.32 kmph
so plane component in west direction=244 sin()=47.32

sin()=0.1933

=11.18 west of north

Vp=244 cos(11.18)+64.7cos(47)=283.5km/h

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