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Projectile from ground level.spends what % of total flight time above a roof of known height?

A rock is thrown upward from ground level with initial velocity Vo, beside a building whose roof height is H.
In terms of Vo, H and g, find what percent of its total flight time the rock is above the roofline.

Solution Preview

Step 1.
<br>To find the total flight time, we use the general function y(t), giving the y coordinate of a projectile as a function of time:
<br>(1) y = yo + Vo t + .5 a t^2
<br>Step 2.
<br>In this event, the rock is at ground level initially and also at the completion of the total flight, so y=0 and also yo= 0. Also, during the whole flight, the acceleration a= -g, the free fall acceleration of a projectile. (Upward is positive, so downward is negative.) Substituting these ...