50 equation would best solve the following problem? tania releases a javelin 1.6 meters above the ground with an initial vertical velocity of 25 meters per second. how long will it take the javelin to hit the ground?

Let be the vertical position of the javelin at time . Once it's thrown in the air, the only force acting on it is gravity, so the javelin would be subjected to a constant downward acceleration of approx. 9.8 meters per second per second. So



Integrating once with respect to , we get



where is the velocity of the javelin. We're told that , so



Integrating again with respect to to get



and we know the javelin was initially thrown 1.6 meters above the ground, or , so we get



So the javelin's position at any time is given by



It will hit ground when . Solve this however you want; you'll find that this will happen at about seconds after the javelin has been thrown.