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Pavel [41]
3 years ago
12

A ball dropped from the top of a building has a height of s =576- 16t2 meters after t seconds. How long does it take the ball to

reach the ground? What is the ball's velocity at the moment of impact?
Mathematics
1 answer:
Step2247 [10]3 years ago
4 0

Answer:

It will take 6 seconds for the ball to reach the ground.

Velocity: -192\frac{\text{m}}{\text{s}}.

Step-by-step explanation:

We have been given that a ball dropped from the top of a building has a height of s =576-16t^2 meters after t seconds.

The ball will hit the ground, when height will be 0 meters, so we will equate height with 0 as:

576-16t^2=0

Let us solve for t.

576-576-16t^2=-576

-16t^2=-576

\frac{-16t^2}{-16}=\frac{-576}{-16}

t^2=36

Taking positive square root of both sides, we will get:

\sqrt{t^2}=\sqrt{36}

t=6

Therefore, it will take 6 seconds for the ball to reach the ground.

To find the ball's velocity at t=6, we will take the derivative of position function and evaluate derivative at t=6.

s=576-16t^2

s'=\frac{d}{dt}(576)-\frac{d}{dt}(16t^2)

s'=0-32t

s'(6)=-32(6)

s'(6)=-192

Therefore, the ball's velocity at the moment of impact would be -192\frac{\text{m}}{\text{s}}.

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50% of the teachers in the meeting were first-year teachers.

Step-by-step explanation:

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2 years ago
On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 30
Troyanec [42]
Assume that the dimensions of the room in the plan are a (width ) by b (length),

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Since the scale is 1:100, a represents 100a, and b represents 100b.

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Answer:  300,000 (square units)


8 0
3 years ago
Amelia's account balance is $16. If she uses her debit card to buy a $32
zimovet [89]

Answer:

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Step-by-step explanation:

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5 0
3 years ago
2sec^2x - secx - 1 = 0
Ivenika [448]
What are you trying to do here?
Solve the graph, or make it appear as something else?

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sec (x) (2sec (x) -2) = 0


Then we're going to separate the two to find the zeros of each because anything time 0 is zero.

sec(x) = 0

2sec (x) - 2 = 0

Now, let's simplify the second one as the first one is already.

Add 2 to both sides:

2sec (x) = 2

Divide by 3 on both sides:

sec (x) = 1


I forgot my unit circle, so you'd have to do that by yourself. Hopefully, I helped a bit though!
8 0
3 years ago
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Answer:

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Step-by-step explanation:

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