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lesya692 [45]
2 years ago
14

2. A football is punted into the air. Its height h, in metres, after t seconds is given by the equation

Mathematics
1 answer:
hichkok12 [17]2 years ago
6 0

Answer:

<u><em>I'll assume the ? is supposed to be t^2</em></u>

See the answers below.

Step-by-step explanation:

h(t) = -4.91t^2 + 24.5t + 1

<u>a) How high is the ball after 1 second?</u>

h(1) = -4.91*(1)^2 + 24.5*(1) + 1

h(1) = 20.59 meters

<u>b) Find the maximum height of the ball to one decimal place.</u>

We can find the maximum height by graphing or by taking the first derivative and setting it equal to zero (the slope is zero at the top of the curve):

  First Derivative

 h(t) = -4.91*(t)^2 + 24.5*(t) + 1

'h(t) = -9.82*(t) + 24.5

0 = -9.82*(t) + 24.5

9.82t = 24.5

t = 2.49 seconds is the time the ball reaches maximum height.  Use that is the equation to find the height:

h(2.49) = -4.91*(2.49)^2 + 24.5*(2.49) + 1

h(2.49) = 31.6 meters

  Graph

See attached graph.  The maximum height occurs at t = 2.49 seconds and the height is 31.6 meters.

<u>c) When does the ball reach its maximum height?</u>

From the first derivative calculation above, t = 2.49 seconds to reach maximum height.  The graph also shows 2.49 seconds.  Better hurry.

d) When does the ball hit the ground?

The can be determined by either direct calculation of from the graph (attached).

Calculation:  

 h(t) = -4.91t^2 + 24.5t + 1

0 (ground) = -4.91t^2 + 24.5t + 1

4.91t^2 - 24.5t - 1 = 0  Solve with the quadratic equation.  I get t = 5.04 seconds

 Graph:

The graph shows 4.95 seconds.  Both agree when rounded to one decimal point:  5.0 seconds.

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Step-by-step explanation:

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I hope that help ✌️
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Collins Middle School has 240 sixth grade students. If the sixth grade is 30% of the total school, how many students are in the
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Answer:

800

Step-by-step explanation:

We can set up a proportion using the information we are given. We know that 240 students corresponds to 30% and that the total number of students, x, corresponds to 100%

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Cross multiply and solve:

240 * 100 = 30x

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3 years ago
Which prism has a greater surface area? 2 prisms. A rectangular prism has a length of 12 inches, height of 8 inches, and width o
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Step-by-step explanation:

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Researches notice a grey whale cruising at a depth of 233 feet below sea level. It rises 73 feet and then comes up another 40 fe
musickatia [10]

Answer:

The whale is at a depth 120 feet below the sea level.

Step-by-step explanation:

A grey whale is cruising at a depth of 233 feet below sea level. The depth below the sea level has the negative position, thus the initial position of the whale is -233.

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