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Talja [164]
2 years ago
13

A skydiver drops her watch as she jumps out of a plane flying at an altitude of 6,400 feet. If the equation for height as a func

tion of time is h(t)=-16t^2+initial height where t is time in seconds and h(t) is height in feet,how many seconds will it take for the watch to hit the ground?
Mathematics
1 answer:
Tems11 [23]2 years ago
6 0

Answer:

To hit the ground, it will take the watch:

  • <u>20 seconds</u>.

Step-by-step explanation:

Making use of the provided equation:

  • <u>h (t) = - 16t ^ 2 + initial height </u>

Which can be modified specifically for this case:

  • <u>h (t) = - 16t ^ 2 + 6400 feet. </u>

Time must be replaced a certain number of times until the value is zero, this can be done one by one, but since it would be too many iterations I will show you some examples and what you could deduce in each case.

<em>With t = 1 second: </em>

  • h (1) = - 16 (1) ^ 2 + 6400 feet = 6384 feet (only the watch has dropped 16 feet)

<em>With t = 7 seconds: </em>

  • h (7) = - 16 (7) ^ 2 + 6400 feet = 5616 feet (has fallen 784 feet)

<em>With h = 15 seconds: </em>

  • h (15) = - 16 (15) ^ 2 + 6400 ft = 2800 feet (3600 ft has fallen, it is not long)

<em>With h = 21 seconds: </em>

  • h (21) = - 16 (21) ^ 2 + 6400 feet = -656 feet (When obtaining a negative number, it is understood that the time was too long, therefore a shorter time must be taken)

<em>With h = 20 seconds: </em>

  • <u>h (20) = - 16 (20) ^ 2 + 6400 feet = 0 feet </u>

<u>Since with 20 seconds the exact value of zero is obtained, this time is the exact time it would take the watch to fall to the ground</u>, since when this time is reached the height (h) will be zero, that is, at ground level .

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