Ajet airliner moving initially at 503 mph
(with respect to the ground) to the east moves
into a region where the wind is blowing at
855 mph in a direction 52◦
north of east.
what is the new speed of the aircraft with
respect to the ground?
answer in units of mph.

The new speed is 1230.28 m/h

Explanation:

The jet airliner moving initially at 503 mph to the east

The wind is blowing at  855 mph in a direction 52° north of east

At first let us distribute the velocity of the wind into east component

and north component

→ The east component is 855 cos(52) m/h

→ The north component is 855 sin(52) m/h

Now we have two components of velocity in the east direction

and one component of velocity in the north direction

The new speed is the resultant of the east and north components

→ The east components are 503 m/h and 855 cos(52) m/h

→ The north component is 855 sin(52) m/h

Add the components of the speeds in direction of east

→ The east component = 503 + 855 cos(52) = 1029.39 m/h

→ The north component = 855 sin(52) = 673.75 m/h

Now we can find the new speed as a resultant speed of the east and

north components

→ The new speed =

→ The new speed = 1230.28 m/h

The new speed is 1230.28 m/h

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm