a car of mass 500 kg is traveling with constant velocity "v" up a straight road inclined at angle 30 degree to the horizontal. if the rate of change of its potential energy with respect to time is 50000 J/s. Find "v".
Answers (1)
Potential energy is mass times g times height in metres (U=mgh). You know U, m and g, so you can work out h (per second). If we say g = 9.8m/s² then h (per second) is 50000/(500*9.8) = 10.2m/s. That's how fast the car is rising vertically, but only one component of its speed is vertical, some is horizontal too.
If you think of the road as the hypotenuse of a triangle, where the opposite is the height, we know that the sine of the angle is opposite over adjacent and the sine of 30° is 0.5. So for every metre travelled along the road, the car rises half a metre in height. Or rather, to rise a metre in height, you have to travel 2m along the road. To rise 10.2m/s, you have to travel 20.4m/s along the road. And that's the speed. 20.4 metres per second. (73.44 km/h or 45.63 mph).
I'm guessing the value of g you've been given is 10m/s², though, to make the calculations easier. If so you'll want to rework this. But at least now you know how.