You have been called to testify as an expert witness in a trial involving a head-on collision. Car A weighs 1515 1515 lb and was traveling eastward. Car B weighs 1125 1125 lb and was traveling westward at 44.0 44.0 mph. The cars locked bumpers and slid eastward with their wheels locked for 20.5 20.5 ft before stopping. You have measured the coefficient of kinetic friction between the tires and the pavement to be 0.750 0.750 . How fast (in miles per hour) was car A traveling just before the collision

Speed = 72.76mph

Explanation:

east direction signifies +

Therefore,

1515E -1125(45) = -2640

F = -2640×0.75 = -1980lbs

so,

-1980lbs = Ma

but m = 2640×g where g = 32.2 ft/s²

so,

a = -(1980/2640g) = -0.75×g = -24.15ft/s² = dv/dt

0 = V-24.15t

V =24.15t

22.5 = Vt -12.07t²

22.5 = 24.15t² - 12.07t² = 12.07t²

t = 1.37 seconds

Therefore,

V = 24.15 × 1.37 seconds = 33.1 ft/s

converting to mph gives

33.1 ft/s = 22.6 mph

now back to momentum

1515 E -1125(45) = 2640 V

1515 E = 50625+59664

Speed = 72.76 mph

72.8mph

Explanation:

east is positive

1515 E -1125(45) = 2640 V

F = 2640*.75 = -1980 pounds

so

-1980 pounds = m a

but m = 2640/g where g = 32.2 ft/s^2

so

a = -(1980/2640)g = -.75 g = -24.15 ft/s^2

= dv/dt

0 = V-24.15 t so V =24.15 t

22.5 = V t -12.07 t^2

22.5 = 24.15 t^2 - 12.07 t^2 = 12.07 t^2

t = 1.37 seconds

so

V = 24.15 * 1.37 seconds = 33.1 ft/s

convert that to mph

33.1 ft/s = 22.6 mph

now back to momentum

1515 E -1125(45) = 2640 V

1515 E = 50625+59664

E = 72.8 mph