Question

The lifting force exerted by the atmosphere on the wings of an airplane in flight varies directly as the surface area of the wings and the square of the plane’s airspeed. A small private plane has a cruising airspeed of 250 miles per hour. In order to obtain 3 times the lifting force, a new plane is designed with a wing surface area twice that of the older model. What cruising speed, to the nearest mile per hour, is planned for the new model?
a.
125 mph
c.
312 mph
b.
280 mph
d.
306 mph

Answer 1

Let F be lifting force. Let A be surface area. Let speed be v
1) Lifting force directly proportional to surface area and square of speed:
F = kAv^2, where k is some constant.

For the small plane:
F = kA(250)^2 ---- (1)

For the new plane:
3F = k2A(v)^2 ---- (2)

Divide equation 1 by 2 to cancel out F and A and k, and find v accordingly.

Answer 2

so its b