12 May '10 03:58

I am in AP Calculus in high school, but I have a question about a physics problem I made up that I

Force gravitational = GMm / (r^2)

Therefore,

Acceleration gravitational = GM / (r^2)

So, here's the problem I came up with. Let's say you take a basketball and travel out into space, approximately 1E10 meters from the center of the Sun, and you release the basketball from rest. Assume that the force of the Sun's gravity is the only force acting on the basketball at any time t. Also assume for the purposes of this problem that the product of G (gravitational constant) and M (mass of the Sun) is 1E20. Finally, assume that the ball is accelerating towards the sun in the negative x direction. Therefore, we know that at time 0, a(0) = -1 m/s^2, v(0) = 0 m/s, and s(0) = 1E10 m.

How would I go about deriving an equation to calculate the velocity of the basketball at any time t? Both time and distance/radius are variables, so again I assume this is a multivariable problem.

Any explanations in addition to any answers would be greatly appreciated.

*assume*is a multivariable calculus problem.Force gravitational = GMm / (r^2)

Therefore,

Acceleration gravitational = GM / (r^2)

So, here's the problem I came up with. Let's say you take a basketball and travel out into space, approximately 1E10 meters from the center of the Sun, and you release the basketball from rest. Assume that the force of the Sun's gravity is the only force acting on the basketball at any time t. Also assume for the purposes of this problem that the product of G (gravitational constant) and M (mass of the Sun) is 1E20. Finally, assume that the ball is accelerating towards the sun in the negative x direction. Therefore, we know that at time 0, a(0) = -1 m/s^2, v(0) = 0 m/s, and s(0) = 1E10 m.

How would I go about deriving an equation to calculate the velocity of the basketball at any time t? Both time and distance/radius are variables, so again I assume this is a multivariable problem.

Any explanations in addition to any answers would be greatly appreciated.