a How high a hill can a car coast up engine disengaged if fr

(a) How high a hill can a car coast up (engine disengaged) if friction is negligible and its initial speed is 86.0 km/h?
m
(b) If, in actuality, a 750 kg car with an initial speed of 86.0 km/h is observed to coast up a hill to a height 14.0 m above its starting point, how much thermal energy was generated by friction?
J
(c) What is the average force of friction if the hill has a slope 2.5° above the horizontal? (Explicitly show on paper how you follow the steps in the Problem-Solving Strategy for energy found on pages 159 and 160. Your instructor may ask you to turn in this work.)
N (down the slope)

Solution

here,

a)

initial speed , u = 86 km/h

u = 23.89 m/s

let the height be h

using conservation of energy

0.5 * m * v^2 = m * g * h

0.5 * 23.89^2 = 9.81 * h

h = 29.1 m

b)

mass , m = 750 kg

initial speed , u = 86 km/h

u = 23.89 m/s

height , h0 = 14 m

the thermal energy was generated by friction , E = 0.5 * m * v^2 - m * g * h0

E = 750 * ( 0.5 * 23.89^2 - 9.81 * 14)

E = 1.1 * 10^5 J

c)

theta = 2.5 degree

let the average force of friction if the hill has a slope 2.5 above the horizontal be ff

ff * h/sin(theta) = E

ff * 14 /sin(2.5) = 1.1 * 10^5

solving for ff

ff = 345.9 J