Question

An $80kg$ person is parachuting and is experiencing a downward acceleration of $2.8m{s}^{-2}$. The mass of the parachute is $5kg$. The upward force on the open parachute is (take, $g=9.8m{s}^{-2}$)

A

$595N$

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B

$675N$

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C

$456N$

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D

$925N$

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Solution

The correct option is A $595N$Step 1: Given Data and assumptions:Mass of person, $M=80kg$ Mass of parachute, $m=5kg$ Downward acceleration, $a=2.8m{s}^{-2}$ Acceleration due to gravity, $g=9.8m{s}^{-2}$Let, the upward force act on the parachute is $F$${F}_{g}$ is taken as positive because it is the force acting due to gravitation. So it is acting in the downward direction.${F}_{a}$ is taken as negative because it is the force acting in the upward direction.Step 2: Formula used:Newton's 2nd law,$F=ma$Where, $F=$the net force acting on the body $m=$mass of the body $a=$acceleration of the bodyStep 3: Calculating the force: $\left(M+m\right)g-F=\left(M+m\right)a$ $⇒$$\left(80+5\right)×9.8-F=\left(80+5\right)×2.8$$⇒$ $F=85×9.8-85×2.8$ $=85×\left(9.8-2.8\right)$ $=85×7$ $=595N$ Hence, option $\left(A\right)$ is the correct answer.

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