Question

Suppose someone throws a rock straight down from the roof of wtimer Hall. If the magitude of the inital downward velocity of the rock was 12 m/s, and the height from which it was thrown was 12 m.How long would it take the rock to hit the ground?

The correct answer is .762 seconds, however I'm not sure how to get there. What formula do you use? Thanks and please explain steps clearly.

Answer 1

DATA:

Solution:

Starting with the following equation:

Here:

Reached Height

Initial position (we take the negative value because the rock is thrown downward)

Initial speed (we take the negative value because the rock is thrown downward)

time

Replacing vales given in DATA into equation (1):

This equation can be written as follows:

Which is a cuadratic equation, solving for :

Here:

Which can be solved using:

Replacing values for a, b and c into equation (2) we have:

solving we obtain:

From which two values are obtained for t:

and

The value of is ignored because negative time has no physical sense. Therefore the solution is for :