Sitting in a second story apartment a physicist notices a ball moving upwards just outside her window the ball is visible for 0.25 seconds as it moves a distance from the bottom to the top of the window. how much time does it take for the ball to reappear

The equation for the height h(t) of an object in free fall at time t with initial velocity v₀ and initial height h₀ is given by:

The change of the height(height of the window) h with time t=0.25s:

Solving for v₀, the velocity of the ball at the bottom of the window:

(i)

The equation for the velocity of an object in free fall with time T:

The moment the ball reaches the top of it's flight the velocity v=0:

(ii)

Setting equations (i) and (ii) equal and solving for T:

The time U it takes the ball to reappear is the difference between the flight time T and twice the time t it takes to cross the window.

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