# 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)=−4.9x2+19.6x+24.a. How long does does it take for the ball to reach its maximum height?     b. What is the maximum height of the ball?

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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)=−4.9x2+19.6x+24.
a. How long does does it take for the ball to reach its maximum height?

b. What is the maximum height of the ball?

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Step 1

(a)

We have to find the time taken by the ball to reach at maximum height.

The height function of the ball is,

Step 2

While graphing the movement of the ball, it will result a parabola.

The highest point on a parabola is at x equal to –b/2a.

Compare the height equation with the equation of a parabola (which is ax2+bx+c).

Then, the value of a is –4.9, b is 19.6 and c is 24.

Substitute -4.9 for a and 19.6 for b in –b/2a.

Step 3

Therefore, the ball reaches its maximum height after 2 seconds.

While substituting 2 for t...

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