- The heights of a ball (in feet) thrown with an initial velocity of 90 feet per second from an initial velocity of 90 feet per second from an initial height of 4 feet is given as a function of time t(in seconds)by s(t)= -16t^2+90t+4
To find the maximum height of the ball, we need to determine the vertex of the parabolic function s(t) = -16t^2 + 90t + 4.
The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula:
t = -b / (2a)
In this case, a = -16 and b = 90. Substituting these values into the formula, we have:
t = -90 / (2(-16))
t = -90 / -32
t ≈ 2.8125
Therefore, the time at which the ball reaches its maximum height is approximately 2.8125 seconds.
To find the maximum height, substitute this time value back into the equation s(t):
s(2.8125) = -16(2.8125)^2 + 90(2.8125) + 4
s(2.8125) ≈ 228.75
Therefore, the maximum height of the ball is approximately 228.75 feet.