A car weighing 1,600 lb travels around a curve at 70 mi/h. The next car to round this curve weighs 2,500 lb and requires the same force as the first car to keep from skidding.

Question

How fast (in mi/h) is the second car traveling? . mi/h

Answer 1

f = 1600k(70^2) = 1600k(4900

= 2500k(v^2) = 1600k(4900)

cancel out the k= constant of proportionality which leaves

1600(4900) = 2500(v^2), solve for v^2

v^2 = 1600(4900)/(2500)

v^2 = 4900(16)/25

take square roots of both sides

v = 70(4)/5=28/5=56 mph

Answer 2

The force is directly proportional to the mass and to the square of the velocity.

So, since the force must be the same in both cases and:

F ~ 1600(70²) and F ~ 2500v² therefore

1600(70²) = 2500v²

7840000 = 2500v²

7840000/2500 = v²

3136 = v²

v = √3136 = 56 mph