How would I solve this question? A ball is thrown upward from the top of a build

Question

How would I solve this question? A ball is thrown upward from the top of a building that is 160feet high. The initial velocity of the ball is 64 feet per second.The height of the ball above the ground is modeled by thefunction                           s(t)= -18t2+72t+216, where t is in seconds and s(t) isthe height above the ground. a. After how many seconds does the ball reach its maximumheight? b. Use your result to part a) to determine the ball's maximumheight. c. After how many seconds does the ball finally reach theground? Round your answer to the nearest tenth of asecond. How would I solve this question? A ball is thrown upward from the top of a building that is 160feet high. The initial velocity of the ball is 64 feet per second.The height of the ball above the ground is modeled by thefunction                           s(t)= -18t2+72t+216, where t is in seconds and s(t) isthe height above the ground. a. After how many seconds does the ball reach its maximumheight? b. Use your result to part a) to determine the ball's maximumheight. c. After how many seconds does the ball finally reach theground? Round your answer to the nearest tenth of asecond.

Explanation / Answer

This is an inverted parabola, with the point of they-intercept equal to the height of the building (ignore the factthat some one throwing the ball releases it 4 or 5 fthigher.) So sketch a graph of the parabola..(I can't get the diagramtool to work). Naturally there is no negative time so part ofthe parabola left of the y-axis is unrealistic. What is the maximum height? put the equation in y =a(x-h)^2 +k where (h,k) is the vertex or maximum of an invertedparabola. The seconds to reach that height are the h ofthe vertex, the max height is the k of the vertex. The x-interept(time) to the right of the max on your graphwill be the time, t. it takes to get to the ground(y-coordinate is 0) In this instance the axis should be labeled t for the x-axisand s(t) for the y-axis.     -- or -- BTW, if you haven't seen the completing the square to get thegraphing form of the parabola, just find the two x-intercepts [oneis real the other only theorectical left of the y axis], If youaverage the x or t values, that will be the time at which the graphreaches maximum. Plug it in for t and solve for s(t) whichwill be the max height. hope either of these two approaches help you understand aswell as get the solution for this problem.

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