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A body was projected vertically upwards at 9.1 meters per second.
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Determine the time taken to reach the maximum height.
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Take π equal to 9.8 metres per second squared.
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In order to solve this question, we will use one of the equations of motion or SUVAT equations: π£ equals π’ plus ππ‘, where π’ is the initial velocity, π£ is the final velocity, π is the acceleration, and π‘ is equal to the time.
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The body is projected vertically upwards at 9.1 meters per second.
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This means that π’ is equal to 9.1.
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At the maximum height, the velocity of the body is zero metres per second.
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Therefore, π£ is equal to zero.
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As gravity is working against the body, π is equal to negative 9.8 metres per second squared.
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And finally, π‘ is the value weβre trying to calculate.
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Substituting in these values into the equation π£ equals π’ plus ππ‘ gives us zero is equal to 9.1 minus 9.8π‘.
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Rearranging this equation gives us 9.8π‘ is equal to 9.1.
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Dividing both sides of the equation by 9.8 gives us a value for π‘ of 9.1 divided by 9.8.
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This is equal to 13 14ths of a second or 0.93 seconds to two decimal places.
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This means that the time taken for a body to reach its maximum height if it is projected vertically upwards at 9.1 meters per second is 13 14ths of a second.