At the circus, an acrobat is shot straight upwards out of cannon that is 2 meters from the ground. After 2.6 seconds, the acrobat lands in a safety net that is 1.076 meters from the ground. The formula h=−4.9t2+vt+(initialheight) gives the height h of the acrobat (in meters) at any time t seconds after being shot from the cannon at a velocity of v meters per second from an initial height (in meters.) Identify each known quantity that can be substituted into the equation to find the missing value in this scenario. For the missing value, select "not given."

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02-09-2021
Mathematics

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At the circus, an acrobat is shot straight upwards out of cannon that is 2 meters from the ground. After 2.6 seconds, the acrobat lands in a safety net that is 1.076 meters from the ground. The formula h=−4.9t2+vt+(initialheight) gives the height h of the acrobat (in meters) at any time t seconds after being shot from the cannon at a velocity of v meters per second from an initial height (in meters.) Identify each known quantity that can be substituted into the equation to find the missing value in this scenario. For the missing value, select "not given."

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oeerivona oeerivona · Answer 1 · 2021-09-06T13:25:20-04:00

To solve for missing values, the number of missing values should be equal to the number of equations. The number of missing values that can be present given only one equation is one missing value

From the question, the known quantities are;

h (known) = 1.076 meters

t (known) = 2.6 seconds

(Initialheight) (known) = 2 meters

The missing value is the velocity;

v (not given)

The reason the above elections are correct is as follows:

The known parameters are;

The (initial) height of the cannon from the ground = 2 meters

The time after which the acrobat lands, t = 2.6 seconds

The height of the safety net on which the acrobat lands, h = 1.076 meters

The formula that gives the height, h, to which the acrobat reaches after being shot from the canon is; h = -4.9·t² + v·t + (initialheight)

Where;

h = The height of the acrobat after being shot or launched from the cannon (known)

The height of the acrobat after the given time, h = 1.076 meters

t = The time in seconds after being shot (Known)

The time is given as 2.6 seconds

v = The velocity with which the acrobat was shot out of the cannon (not given)

The velocity with which the acrobat was shot out of the cannon is the missing value

(Initialheight) = The initial height of the acrobat before he was shot from the cannon (known)

The initial height of the was given as the height of the cannon off the ground which is 2 meters

Therefore, the known quantity or quantities that can be substituted into the equation to find the missing value in the scenario are;

h (known) = 1.076 meters

t (known) = 2.6 seconds

(Initialheight) (known) = 2 meters

The missing value is the velocity, v;

v (not given)

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