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3 years ago

How long will it take the ball to reach the ground

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

8 0

When the ball reaches the ground, its height is 0.
We set the height function equal to zero and solve for t, the time.

h = -16t^2 + 250

-16t^2 + 250 = 0

16t^2 - 250 = 0

$(4t + \sqrt{250})(4t - \sqrt{250}) = 0$

$4t + \sqrt{250} = 0$ or $4t - \sqrt{250} = 0$

$4t = -\sqrt{250}$ or $4t = \sqrt{250}$

$t = -\dfrac{\sqrt{250}}{4}$ or $t = \dfrac{\sqrt{250}}{4}$

We discard the negative solution since time must be positive.
The positive solution is

$t = \dfrac{\sqrt{250}}{4} \approx 4.0$

Answer: 4.0 seconds

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Read 2 more answers

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To solve this question, we need to understand the normal probability distribution and the central limit theorem.

A reminder is that the standard deviation is the square root of the variance.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

$\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5$

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This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So

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