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kicyunya [14]
3 years ago
14

A ball is kicked 4 feet above the ground with an initial vertical velocity of 55 feet per second. The function h(t)=−16t2+55t+4

represents the height h (in feet) of the ball after t seconds. Using a graph, after how many seconds is the ball 30 feet above the ground? Round your answers to the nearest tenth.
I would like to know both the answer and the steps to get there please and i need it asap. Thank you!

Mathematics
1 answer:
kramer3 years ago
5 0

<u>Given</u>:

A ball is kicked 4 feet above the ground with an initial vertical velocity of 55 feet per second.

The function h(t)=-16t^2+55t+4 represents the height h(in feet) of the ball after t seconds.

We need to determine the time of the ball at which it is 30 feet above the ground.

<u>Time:</u>

To determine the time that it takes for the ball to reach a height of 30 feet above the ground, let us substitute h(t) = 30, we get;

30=-16t^2+55t+4

26=-16t^2+55t

Adding both sides of the equation by 16t², we get;

16t^2+26=55t

Subtracting both sides of the equation by 55t, we have;

16t^2-55t+26=0

Let us solve the quadratic equation using the quadratic formula, we get;

t=\frac{-(-55) \pm \sqrt{(-55)^2-4(16)(26)}}{2(16)}

t=\frac{55 \pm \sqrt{3025-1664}}{32}

t=\frac{55 \pm \sqrt{1361}}{32}

t=\frac{55 \pm 36.89}{32}

t=\frac{55 + 36.89}{32} \ or \ t=\frac{55- 36.89}{32}

t=\frac{91.89}{32} \ or \ t=\frac{18.11}{32}

t=2.9 \ or \ t=0.6

The value of t is t = 0.6 because this denotes the time taken by the ball to reach a height of 30 feet from the ground.

Therefore, the time taken by the ball to reach a height of 30 feet above the ground is 0.6 seconds.

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