Question : An aeroplane is flying with velocity Vp (=10 m/s towards east) with respect to the ground through motionless air and Vm is the wind velocity with respect to ground. The total velocity of the aeroplane is V=Vp+Vw.
The magnitude of the velocity if often called speed. The heading of the plane is the direction in which the nose of the plane points. In fact, it is the direction in which the engine propels the plane.
i) If the wind blows with velocity 25 m/s northwards and the pilot adjusts the heading of the plane so that the total velocity of the plane is Eastwards. By what angle does the new heading differ from due east?
a) sin-1(25/100)
b) cos-1(25/100)
c) tan-1(25/100)
d) cot-1(25/100)
ii) If the wind velocity blows with velocity 25 m/s northwards, the plan velocity is detected from east by an angle
a) sin-1(25/100)
b) cos-1(25/100)
c) tan-1(25/100)
d) cot-1(25/100)
iii) The total speed of the plane w.r.t ground in m/s is
a) 100sinΦ
b) 100cosΦ
c) 100cosecΦ
d) 100secΦ
iv) Suppose θ is the angle by which plane velocity is detected from east, then the total speed of the plane in m/s is
a) 100sinθ
b) 100cosθ
c) 100cosecθ
d) 100secθ
v) If the wind blows with the velocity 25 m/s w.r.t. ground southwards, total speed of the plane is:
a) 75 m/s
b) more than 75 m/s but less than 100 m/s
c) 100 m/s
d) more than 100 m/s
Doubt by Muskan
Solution : Coming Soon.