An object in launched directly upward at 64 feet per second from platform 80 feet high. its height is represented by the equation s ( t ) =- 16t +64t+80. What will be the object's maximum height?
To find the maximum height of the object, we need to determine the vertex of the quadratic equation for height (s) with respect to time (t).
The equation for height (s) as a function of time (t) is given as:
s(t) = -16t^2 + 64t + 80
We can see that this is a quadratic equation in the form of: s(t) = at^2 + bt + c, where a = -16, b = 64, and c = 80.
The vertex of a quadratic equation can be found using the formula: t = -b / (2a).
In this case, t = -64 / (2 * -16) = -64 / -32 = 2.
So, the object reaches its maximum height after 2 seconds.
To find the maximum height, substitute the value of t back into the equation:
s(2) = -16(2)^2 + 64(2) + 80
= -16(4) + 128 + 80
= -64 + 128 + 80
= 144
Therefore, the object's maximum height is 144 feet.
To find the maximum height of the object, we need to determine the vertex of the parabolic function represented by the equation s(t) = -16t^2 + 64t + 80.
The vertex of a parabola with the equation in the form s(t) = at^2 + bt + c is given by the formula t = -b / (2a).
In this case, a = -16 and b = 64. Plugging these values into the formula, we get:
t = -64 / (2 * -16)
t = -64 / -32
t = 2
The object reaches its maximum height after 2 seconds.
To find the maximum height, we substitute the value of t into the equation:
s(t) = -16t^2 + 64t + 80
s(2) = -16(2)^2 + 64(2) + 80
s(2) = -16(4) + 128 + 80
s(2) = -64 + 128 + 80
s(2) = 144
Therefore, the object's maximum height is 144 feet.