I need help solving this problem along with how to solve it.

Question

The force required to keep a car from skidding in a turn

varies jointly with the mass of the car m, the square of its

speed v, and the curvature k of the turn. The curvature is the

reciprocal of the radius of the turn, k=1/r. Suppose it takes

2800 lb of force to keep an 1800-lb car from skidding at 45

mi/h on a curve with radius 425 ft. What force is needed to

keep the car from skidding at 50 mi/h on a curve with a radius of

440 ft?

Answer 1

Force (F) varies jointly with the mass (m), the square of the speed (v), and the curvature of the turn (k):

Let's let "C" = the constant of proportionality, then:

F = Cmv²k

But k = 1/r so we get:

F = Cmv²/r

Let F = 2800

m = 1800

v = 45

r = 425

Then 2800 = C(1800)(45²)/425 or C = 2800(425)/(1800•45²) = 0.3264746228

Our equation then is F = 0.3264746228mv²/r when m is in pounds, v is in mi/h and r is in feet and F is in pounds.

F = 0.3264746228(1800)(50²)/440

F = 3339 pounds