Jim is flying due east in a 747 which has a cruising airspeed of 500mph. The plane is in a jet stream blowing at 100 mph , 25 degree east of south.
If he got out of his seat and run toward the front of the plane at 10mph(before he tackled to the ground by an airspeed), what's his speed with respect to the ground and the velocity of the plane with respect to ground.

Question

Jim is flying due east in a 747 which has a cruising airspeed of 500mph. The plane is in a jet stream blowing at 100 mph , 25 degree east of south.
If he got out of his seat and run toward the front of the plane at 10mph(before he tackled to the ground by an airspeed), what's his speed with respect to the ground and the velocity of the plane with respect to ground.

anonymous · Answer

Vectors! To the vectors belong the spoils?

x-direction is east: 500 + 100 sin(25) = 542.2 m/s east component of velocity 

y-direction is north : 0 - 100 cos(25) = -90.6 m/s south 

v is sqrt(sum of squares) = sqrt(542.2^2 + 90.6^2) = 550 mi/hr

Direction of  is arc tan(x/y) here = arc tan (90.6/542) = 9.5o south of east.

Running up the aisle makes kid's vel. wrto ground 550+10 = 56 mph same direction.