To find the time it takes for the ball to reach its maximum height, you need to determine the value of "t" where the equation h(t) = -16t^2 + 20t + 2 reaches its maximum point.
In this case, the height function is a quadratic equation in the form h(t) = at^2 + bt + c, where a = -16, b = 20, and c = 2. The maximum point of a quadratic function occurs at the vertex, which is found using the formula t = -b / (2a).
Plugging in the values, we have t = -20 / (2*(-16)). Simplifying this, we get t = -20 / -32 = 5/8 = 0.625.
Rounding to the nearest hundredth, the ball takes approximately 0.63 seconds to reach its maximum height.
To find the maximum height, you need to substitute the value of "t" into the height function h(t).
Plugging in t = 0.63, we have h(0.63) = -16*(0.63)^2 + 20*(0.63) + 2.
Calculating this, h(0.63) ≈ -6.45 + 12.6 + 2 ≈ 8.15.
Rounding to the nearest hundredth, the ball reaches its maximum height of approximately 8.15 feet.