The force needed to keep a car from skidding on a curve varies inversely as the radius of the curve and jointly as the weight of the car and the square of the car's speed. Suppose that 245 pounds of force keeps a 2000-pound car from skidding on a curve of radius 600 ft at 35 mph. What force would keep the same car from skidding on a curve of radius 900 ft at 45 mph?
Let F be the force needed to keep the car from skidding, w be the weight of the car, r be the radius of the curve, and s be the car's speed. From the problem, we have the equation F = k * w * s^2 / r, where k is the constant of proportionality. We can find k by plugging in the given data:
245 = k * 2000 * 35^2 / 600
Solving for k, we get:
k = 245 * 600 / (2000 * 35^2)
k ≈ 0.025
Now we have the constant of proportionality, we can solve for the force required for the 900 ft radius and 45 mph:
F = 0.025 * 2000 * 45^2 / 900
F ≈ 450
So, the force required to keep the car from skidding on a curve of radius 900 ft at 45 mph is approximately 450 pounds.