What equation describes the path of a ball tossed in the air?
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✔✔The forces are never balanced, as there is only ever one force - gravity.
✔✔The key is to remember Newton's second law: F=maF=ma. Force and acceleration are paired, not force and velocity. Knowing just an object's current velocity tells you nothing about what forces are acting on it.
✔✔There are two ways to see how the velocity goes to zero. Either the initial impulse (instantaneous transfer of momentum) is depleted by a force applied over time,
✔✔mΔv=∫F dt,mΔv=∫F dt,
✔✔or the initial kinetic energy is depleted by a force applied over a distance,
✔✔12mΔ(v2)=∫F dx.12mΔ(v2)=∫F dx.
✔✔In both cases, the force of gravity is acting continuously to slowly cancel the initial velocity, and there is nothing that turns off this force at the apex of the trajectory.
✔✔The forces are never balanced, as there is only ever one force - gravity.
✔✔The key is to remember Newton's second law: F=maF=ma. Force and acceleration are paired, not force and velocity. Knowing just an object's current velocity tells you nothing about what forces are acting on it.
✔✔There are two ways to see how the velocity goes to zero. Either the initial impulse (instantaneous transfer of momentum) is depleted by a force applied over time,
✔✔mΔv=∫F dt,mΔv=∫F dt,
✔✔or the initial kinetic energy is depleted by a force applied over a distance,
✔✔12mΔ(v2)=∫F dx.12mΔ(v2)=∫F dx.
✔✔In both cases, the force of gravity is acting continuously to slowly cancel the initial velocity, and there is nothing that turns off this force at the apex of the trajectory.
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