Final answer:
The speed of an object dropped from a height of 660 meters, 10 seconds after being dropped, is 98 m/s in a downward direction. This is found using the derivative of the height function. Kinematic equations are significant in determining such motions.
Step-by-step explanation:
To determine the speed of an object 10 seconds after it has been dropped from a height of 660 meters, we can use the given mathematical expression for its height: 660 - 4.9t2. The speed of the object at any given time is the first derivative of this position function with respect to time, which represents the object's velocity.
The velocity (v) as a function of time (t) is given by the derivative of the position (s), which is v = ds/dt = -9.8t. So the speed 10 seconds after being dropped is v = -9.8 * 10 = -98 m/s (the negative sign indicates the direction of motion is downwards).
Analyzing factors affecting the object's motion includes gravity, which is causing the acceleration at 9.8 m/s2 downwards, and assuming no air resistance is present. The relationship between speed and time is linear for an object in free fall due to constant acceleration. This example highlights the significance of the kinematic equations and how they can be used to describe motion mathematically.