Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# a ball is thrown from a balcony that is 20meters above ground. The path of the ball is described by the equation h=a(x-5)^2+22.5.?

Update:

I would like to know the answer to a and c only. I am not sure how to get that answer Relevance

a) The ball falls off from the balcony, which is 20 m high. At the very beginning, there's no horizontal displacement, so: x = 0; h = 20. Therefore:

20 = a * (0 - 5)^2 + 22.5 ===> 20 = a * 25 + 22.5 ===> 20 - 22.5 = 25a ===>

===> -2.5 = 25a ===> a = -2.5/25 = -0.1

c) The equation that describes the path is: h = -0.1 * (x - 5)^2 + 22.5.

x = 5 is the abscissa of the vertex; y = 22.5 is the ordinate of the vertex.

(*) The maximum height reached by the ball is given by the ordinate of the vertex of the parabola that describes the path. Hence: h_max = 22.5 m.

(**) The horizontal displacement of the ball (when it reaches the maximum height) is given by the abscissa of the parabola that describes the path. Hence: x = 5 m.

• a) At the start h = 20 and x = 0

so, 20 = a(0 - 5)² + 22.5

=> 20 = 25a + 22.5

i.e. 25a = -2.5

Hence, a = -2.5/25 => -0.1

c) The function is in vertex form, so maximum value occurs when the quadratic term is zero

Hence, when x = 5 metres

Then, h = -0.1(5 - 5)² + 22.5

i.e. h = 22.5 metres

A sketch is below.

:)> • Anonymous
1 month ago

Is there any reason you don't pick Best Answers?