Coasting up a driveway with snow -- cons. of energy 1. The problem statement, all variables and given/known data Your Physics teacher drives an ideal frictionless car of mass 1000kg which coasts along the level road to his home at a constant speed of 48km/h with the engine turned off. It then coats up 40m his sloping driveway and comes to rest at the top, without any braking required. One day he found that his engine had to develop 30 kilowatts of power to maintain a stead speed of 48km/h on the level due to a layer of loose snow on the road. He quickly calculated the new speed required for him to coast up his driveway with the engine switched off at the bottom as usual. He assumed that the snow on the hill would give the same constant retarding force as the snow on the level. What was the new speed? 2. Relevant equations ETi=ETf Ek=1/2 mv2 Eg=mgh P=E/T S=D/T 3. The attempt at a solution I drew a diagram and attached it. 48km/h=13.3m/s 30kW=30 000w Without snow T=D/S T=40m/13.3m/s T=3.0s ETi=ETf 1/2 mv2=mgh 1/2 v2=gh v2/2g=h (13.3)2/2(9.8)=h h=9m θ=sin-1(9/40) θ=0.23° With snow P=E/T E=PT E=(30 000W)(3.0s) E=90 000J E=1/2mv2 √2E/m=v v=√2(90 000)/1000 v=13.4m/s I'm not sure though... so does that mean there's snow on all of it? When there is snow, he has his engine turned on throughout the level but instantaneously turns it off before he goes up the driveway??? I feel that the angle of the driveway is too small. So, if it reaches the top off the driveway, something must be 0? The acceleration would be 0 wouldn't it?