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A car coasts engine off up a 30 degree grade if the speed of the car is 25 meters per second at the bottom of the grade what is the distance traveled by the car before it comes to rest?
DrGoood
At the bottom, the car has kinetic energy of ½mv2. At the top, the car has kinetic energy of 0. If we ignore friction and wind resistance, the initial kinetic energy is converted to gravitational potential energy of mgh, where the m is again the mass of the car, g is the acceleration of gravity, and h is the vertical change in position of the car. Solving the two equations for h, we get
h=½v2/g=(0.5)(25 m/s)2/(9.8 m/s2)=31.888 m
To find the distance traveled along the road, we use a bit of trigonometry: sin(30°) = h/d = 0.5, so d = 2h = 63.776 meters
Of course, the actual value will be less, due to the friction and wind resistance that we ignored in our calculations.
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