An object moving due to gravity can be described by the motion equation y=y0+v0t−12gt2, where t is time, y is the height at that time, y0 is the initial height (at t=0), v0 is the initial velocity, and g=9.8m/s2 (the acceleration due to gravity). if you stand at the edge of a cliff that is 75 m high and throw a rock directly up into the air with a velocity of 20 m/s, at what time will the rock hit the ground? (note: the quadratic formula will give two answers, but only one of them is reasonable.) view available hint(s)

6.45 s

Explanation:

We have the following equation:

(1)

Where:

is the height when the rock hits the ground

the height at the edge of the cilff

the initial velocity

acceleration due gravity

time

 (2)

Rearranging the equation:

(3)

At this point we have a quadratic equation of the form , and we have to use the quadratic formula if we want to find  :

 (4)

Where , ,

Substituting the known values and choosing the positive result of the equation:

 (5)

 This is the time it takes to the rock to hit the ground

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