Question

The strings of a parachute can bear a maximum tension of 75 kg-weight. By what minimum acceleration can a person of 96 kg descend by means of this parachute?

Answer 1

Hint : When the person is falling, he is accelerating downwards due to gravitational acceleration. The net force acting on the string will be due to the sum of the weight of the person and the force associated with its acceleration.

Complete step by step answer:
When a person is falling by means of a parachute, the net force in the downwards direction will be due to the sum of the gravitational acceleration acting on the block and the weight of the block.
The force in the upwards direction will be due to the tension in the string of the parachute. As we know that the person will be slowly falling towards the ground, the net acceleration of the person will be in the same direction as the gravitational acceleration of the object.
Now, we know that the weight of the person will be $ W = mg $ .
If we denote the tension in the strings by $ T $ and the acceleration of the person by $ a $ , the equation of motion will be
 $ T = ma + mg $
Substituting the $ m = 96\,kg $ and $ g = 9.8\,m/{s^2} $ and $ T = 75\,kg $ , we get
 $ 75 = 96 \times a + 75(9.8) $
Solving for $ a, $ , we get
 $ a = 2.45\,m/{s^2} $ .

Note:
Here we have neglected the air resistance experienced by the person which will also exert an upwards force depending on the velocity of the person. This acceleration is the upper limit of the tension that can be handled by the strings of the parachute. In reality, when falling with a parachute, the net acceleration reaches zero after some time after the parachute is opened. This is because the person will eventually stop accelerating and at this point, the tension in the string will be equal to the weight of the person.