Answer:
The given equation is H = -16t^2 + 64t + 60, where t is the elapsed time in seconds. This equation represents the height, H, of an object thrown upward from the ground with an initial velocity of 64 ft/s.
Explanation:
1. The term -16t^2 represents the effect of gravity on the object. Since the coefficient is negative, it indicates that the object is moving upward against the force of gravity. The square of the time, t^2, shows that the effect of gravity increases as time passes. 2. The term 64t represents the initial velocity of the object. The coefficient 64 indicates that the object was thrown upward with an initial velocity of 64 ft/s. The time, t, shows the effect of the initial velocity on the height. 3. The constant term 60 represents any additional height above the ground at the start. It could be the height from which the object was thrown or any elevation from the ground. By plugging different values of t into the equation, you can find the corresponding heights at different times. For example, if you substitute t = 0, the equation becomes H = -16(0)^2 + 64(0) + 60 = 60. This means that at the start (t = 0), the object is at a height of 60 feet above the ground. To find the maximum height reached by the object, we need to determine the vertex of the parabolic equation. The vertex is given by the formula t = -b/(2a), where a and b are the coefficients of t^2 and t, respectively. In this case, a = -16 and b = 64. Substituting these values into the formula, we get t = -64/(2(-16)) = 2 seconds. This means that the object reaches its maximum height after 2 seconds. To find the maximum height, substitute t = 2 into the equation: H = -16(2)^2 + 64(2) + 60 = 64 feet. Therefore, the object reaches a maximum height of 64 feet above the ground after 2 seconds. I hope this explanation helps you understand the meaning of the given equation and how to interpret it in the context of elapsed time and height. Let me know if this helped!