Question

We are standing on the top of a 896 feet tall building and launch a small object upward. The object's

vertical position, measured in feet, after t seconds is h(t) = – 16t+ 160t + 896. What is the highest
point that the object reaches?

Answer 1

The maximum height reached by the object launched from a 896 feet tall building is 1296 feet. This is found by using the vertex formula to determine the time at which the object reaches its apex and then substituting this time back into the height function.

Step-by-step explanation:

To determine the highest point that the object reaches when launched from the top of a building, we'll need to analyze the given quadratic equation for the vertical position h(t) = -16t2 + 160t + 896. This quadratic equation represents the height (h) as a function of time (t). The highest point, also known as the apex, occurs at the vertex of the parabola described by the equation. Since the coefficient of t2 is negative, the parabola opens downward, making the vertex the maximum point.

To find the time at which the object reaches its maximum height, we use the vertex formula t = -b/(2a), where a is the coefficient of t2 and b is the coefficient of t. In this equation, a = -16 and b = 160. Plugging these values into the formula, we get t = -160/(2 × -16) = 5 seconds. This is the time at which the object reaches its apex.

Now, to find the maximum height, we substitute this time into the original height function: h(5) = -16(5)2 + 160(5) + 896 which simplifies to h(5) = -16(25) + 800 + 896. Calculating further, we get h(5) = -400 + 800 + 896, so the maximum height reached is 1296 feet.

Answer 2

h(t)=-16t+160t+896
Use -b/2a
a=-16
b=160
c=896
t= -160/2(-16) = 5 sec
It will reach it’s highest point at 5 seconds
= -16(5)^2 +160 (5) + 896
= 1296

The Answer is
1296ft