Question

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.How long does does it take for the ball to reach its maximum height? What is the maximum height of the ball?(Round your answer to three decimal places)

Answer 1

Answer:

It would take 2 second to reach its maximum height.

The maximum height of the ball is 43.6 meters above the ground.

Step-by-step explanation:

Consider the provided function.

$h(x)=-4.9x^2+19.6x+24$

The above function's graph is a downward parabola and the maximum of the downward parabola is at its vertex.

We can find the x coordinate of the function using the formula: $\frac{-b}{2a}$

Substitute a=-4.9 and b=19.6 in $\frac{-b}{2a}$

$x=\frac{-19.6}{2(-4.9)}$

$x=\frac{19.6}{9.8}$

$x=2}$

Hence, it would take 2 second to reach its maximum height.

Substitute x=2 in above formula.

$h(2)=-4.9(2)^2+19.6(2)+24$

$h(2)=-19.6+39.2+24$

$h(2)=43.6$

Hence, the maximum height of the ball is 43.6 meters above the ground.