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Bumek [7]
2 years ago
14

In the air, it had an average speed of 16 1616 m/s m/sstart text, m, slash, s, end text. In the water, it had an average speed o

f 3 33 m/s m/sstart text, m, slash, s, end text before hitting the seabed. The total distance from the top of the cliff to the seabed is 127 127127 meters, and the stone's entire fall took 12 1212 seconds.
Mathematics
1 answer:
Diano4ka-milaya [45]2 years ago
8 0

Answer:

t_a = 7 s

t_w = 5 s

Step-by-step explanation:

Given:

- The average speed in air v_a = 16 m/s

- The average speed in water v_w = 3 m/s

- The total distance D = 127 m

- The total time T = 12 s

Find:

How long did the stone fall in air and how long did it fall in the water?

Solution:

- Lets time taken by stone to drop through air as t_a = t_a.

- The time taken in water would be t_w = (12 - t_a)

- The total distance covered can be calculated as:

                            D = v_a*t_a+ v_w*(12 - t_a)

                            127 = 16*t_a + 3*(12 - t_a)

Simplify and solve for t:

                            91 = 16*t_a - 3t_a

                            13*t_a = 91

                            t_a = 7 s

                            t_w = 5 s

                           

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h(3)=-16(3)^{2} +63(3)+4=49\ ft

Part b) What is the maximum height of the ball? Round to the nearest foot.

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Convert the function into a vertex form

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Group terms that contain the same variable, and move the constant to the opposite side of the equation

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h(t)-4=-16(t^{2} -(63/16)t)

Complete the square. Remember to balance the equation by adding the same constants to each side

h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})

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Rewrite as perfect squares

h(t)-(67,600/1,024)=-16(t-(63/32))^{2}

h(t)=-16(t-(63/32))^{2}+(67,600/1,024)

the vertex is the point (1.97,66.02)

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The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

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h(t)=-16t^{2} +63t+4

For h(t)=0

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using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

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