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.
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?
1 answer