Kinetic energy = Potential energy
(1/2)mV^2 = mgh
where
m = mass of the car
V = velocity of the car = 15 m/s (given)
g = acceleration due to gravity = 9.8 m/sec^2 (constant)
h = vertical distance travelled by car = d(sin 19)
d = distance travelled by the car along the incline
Substituting values,
(1/2)(m)(529) = m(9.8)h
and since "m" appears on both sides of the equation, it will simply cancel out, hence the above becomes
(1/2)(529) = 9.8h
h = 225/19.6 = 26,98 m
Let
d = distance that the car will coast up the hill before coming down
h/d = sin 19
and therefore,
d = h/sin 19
and substituting values,
d = 26,98/sin 19
d = 82,870 m --- after coasting up the hill for this distance, the car will start to roll down.
