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3 years ago

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A ball is thrown strait up from the top of a 64 foot tall building with an initial speed of 48 feet per second. The height of th

e ball as a function of time can be modeled by the function h(t)=-16t^2+48t+64. At what other time will the ball be at a height of 64 feet? How long will it take for f ball to reach its maximum height? What is he maximum height reached by the ball? How long willlit take for the ball to hit the ground?

1 answer:

Mrrafil [7]3 years ago

4 0

Answer:

see below

Step-by-step explanation:

h(t)=-16t^2+48t+64

Find when h(t) = 64

64 = -16t^2+48t+64

Subtract 64 from each side

0 = -16t^2+48t

Factor

0 = -16t( t-3)

Using the zero product property

-16t =0 t-3 =0

t=0 and t=3

Other than at t=0, so at t=3 seconds

How long will it take for f ball to reach its maximum height?

Find the vertex

t = -b/2a = -48 / ( 2 * -16) = -48/ -32 = 1.5 seconds

It will reach the maximum height at 1.5 seconds

What is the maximum height reached by the ball?

The height will be

h(1.5) = -16*(1.5)^2+48(1.5)+64

= -36+72+64

= 100

The maximum height is 100 ft

How long will it take for the ball to hit the ground?

h(t) =0

0=-16t^2+48t+64

Factor

0 = -16( t^2 - 3t -4)

0=- 16( t-4) (t+1)

Using the zero product property

t-4=0 t+1=0

t =4 t = -1

Since time cannot be negative

t=4 seconds

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Step-by-step explanation:

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We can calculate the sample mean and deviation with these formulas:

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$s_{2}=5.559$ represent the sample standard deviation for the sample 2

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$n_{2}=10$ sample size selected 2

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

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Alternative hypothesis: $\mu_{1} < \mu_{2}$

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t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

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