Answer in Algebra
A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t)= -4.9t^2+ 24t + 8 What is the height of the building? What is the maximum height reached by the ball? How long does it take to reach maximum height? Also, find a rigorous algebraic solution for the problem.
The height of the building is given when t=0
thus h(0)= -4.9 (0)2 24 (0) + 8 = 8
Therefore, the height of the building = 8
At maximum height the first derivative of the function is equal to zero
hence h'(x)=-9.8t +24=0;
Thus time taken to reach the maximum height, t= 24/9.8 = 2.449.
Hence the maximum height reached by the ball = h(2.449) = -4.9 (2.449)2 +24 (2.449) + 8 = 37.3878
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