# Conservation of energy

If a 3 kg ball is thrown straight up at 40 m/s, using energy conservation, calculate how high the ball would go if there was no wind resistance.

I was told this could not be calculated. Is that true? and if so, why?

## Answers and Replies

Homework Helper
why not, loss in KE = gain in PE ?

If you want to add in air resistance, you have to account for the cross-sectional area of the ball (A), as a sheet of paper will fall slower than a crumpled up piece. Similarly, a styrofoam ball will encounter more resistance than a rubber ball, so density (d) is inversely proportional to the air resistance. Next, stick your hand out when you're walking. Compare it to sticking your hand out when you're running or in a car. Speed (v) is thus proportional to air resistance. We're insterested in the distance the ball will travel. m is the mass of the ball. So far we have the rudimentary 1-dimensional net force equation ma = mg - A*d*v. But v is not a constant, it is a function of time, so we have to solve the differential equation m*dv/dt = - mg - A*d*v for speed v or m*d2x/dt2 = - mg - A*d*dx/dt for distance x. This simple model has many more refinements placed on it based on the speed of the object and the type of resistance, but solving it will already allow you to see simple behavior like terminal velocity. 