Need to find time it falls?

Question

A ball falls from the top of a roof and its initial speed is 20m/s and the acceleration of gravity is 9.8m/s^2. How do I find how long it takes the first ball to hit the ground?

Answer 1

The equation of motion is
y(t)=h+vi*t-.5*g*t^2

h is the height of the building
vi is initial velocity, which is a vector. If the ball is thrown straight up, then vi= 20 m/s, if the ball is thrown straight downward, then vi=-20 m/s; if the ball is thrown upward at an angle th w/r/t horizontal, then vi=20*sin(th), and so on.
plug in h, vi, and g, set y(t)=0, and solve for t. Since it is a quadratic, use the positive root.

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