Hello,
I did this question for homework, but my teacher said it was wrong and she didn't explain how it was supposed to be done. So could you please tell me how I am supposed to do this step by step?
"A baseball is thrown from the top of a building and falls to the ground below. The height of the baseball above the ground is approximated by the relation h = -5t2 + 10t + 15, where h is the height above the ground in metres and "t" is the elapsed time in seconds. Determine the maximum height that is reached by the ball.
Thank you very much!
the graph is a parabola, with vertex at t=1
h(1) = 20
see a picture and analysis at
http://www.wolframalpha.com/input/?i=-5t^2+%2B+10t+%2B+15
Sure! I'd be happy to help you with this problem step by step.
To determine the maximum height reached by the ball, we need to find the vertex of the parabolic equation h = -5t^2 + 10t + 15. The vertex of a parabola is the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards.
To find the vertex, we can use the formula t = -b / (2a), where a, b, and c are the coefficients of the quadratic equation in the form h = at^2 + bt + c.
In this case, a = -5, b = 10, and c = 15. Let's substitute these values into the formula:
t = -10 / (2 * -5)
t = -10 / -10
t = 1
So, the time at which the ball reaches its maximum height is t = 1 second.
To find the maximum height, we can substitute this value of t back into the equation h = -5t^2 + 10t + 15:
h = -5(1)^2 + 10(1) + 15
h = -5 + 10 + 15
h = 20
Therefore, the maximum height reached by the ball is 20 meters.
I hope this helps! Let me know if you have any further questions.