a stone is thrown up from a height of 30 ft. The initial velocity is 60 ft/sec. If s(t)= -16t^2+60t+30. Find the time at which the stone riches its maximum height and find the maximum height
To find the time at which the stone reaches its maximum height, we need to find the vertex of the parabolic equation s(t) = -16t^2 + 60t + 30.
The vertex of a parabola in the form of "y = ax^2 + bx + c" can be found using the formula t = -b / (2a).
In this case, a = -16 and b = 60:
t = -60 / (2 * -16) = 60 / 32 = 1.875
Therefore, the stone reaches its maximum height at t = 1.875 seconds.
To find the maximum height, substitute this value of t back into the equation s(t):
s(1.875) = -16(1.875)^2 + 60(1.875) + 30
Simplifying this equation gives:
s(1.875) ≈ 83.90625
Hence, the maximum height reached by the stone is approximately 83.90625 feet.