Answer :
Final answer:
The object was released from a height and it took 3.79 seconds for it to reach the ground. This conclusion was derived from applying the quadratic formula to the given equation that describes the object's motion.
Explanation:
This is a physics problem that uses quadratic equations from Mathematics. The given equation (-16*t²+218-154) represents the object's height at different times. Applying the quadratic formula to this equation gives t = 3.79 s and t = 0.54 s.
We need to interpret these solutions in the context of the problem. The object cannot have two different heights at the same time so the two solutions represent the times at which the object passes through the same height on its way up and on its way down. Since we are interested in the time it takes for the ball to be released (i.e., from the moment it is dropped until it hits the ground), we take the longer solution. Therefore the time taken is t = 3.79 seconds.
This topic ties Mathematics and Physics together as it uses quadratic equations to solve a real-world problem.
Learn more about Quadratic Equations in Physics here:
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