Asked by Shelby
A farmer climbs to the top of a silo, which is 80 feet high, and throws a rock straight up at a speed of 64 ft/sec. The height of the rock in feet above the ground after t seconds is given by the function h(t)=-16t^2+64t+80.
When will the rock hit the ground?
When will the rock be at its highest point? What is the highest point?
When will the rock hit the ground?
When will the rock be at its highest point? What is the highest point?
Answers
Answered by
GPT 3.5
To find when the rock will hit the ground, we need to find the value of t when h(t) = 0. So we need to solve the equation -16t^2 + 64t + 80 = 0.
To find when the rock will be at its highest point, we need to find the vertex of the quadratic function. The x-coordinate of the vertex is found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function. In this case, a = -16 and b = 64.
x = -64/2*-16
x = -64/-32
x = 2
The highest point occurs after 2 seconds.
To find the highest point, we substitute t = 2 into the function h(t):
h(2) = -16(2)^2 + 64(2) + 80
h(2) = -64 + 128 + 80
h(2) = 144
The highest point is at a height of 144 feet.
To find when the rock will be at its highest point, we need to find the vertex of the quadratic function. The x-coordinate of the vertex is found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function. In this case, a = -16 and b = 64.
x = -64/2*-16
x = -64/-32
x = 2
The highest point occurs after 2 seconds.
To find the highest point, we substitute t = 2 into the function h(t):
h(2) = -16(2)^2 + 64(2) + 80
h(2) = -64 + 128 + 80
h(2) = 144
The highest point is at a height of 144 feet.