What is the mass of a paratrooper who experiences an air resistance of 400 N and an acceleration of 4.5 m/s2 during a parachute jump.
m=F/a
To find the mass of the paratrooper, we need to use Newton's second law of motion. The formula is given by:
Force (F) = mass (m) x acceleration (a)
In this case, the net force acting on the paratrooper is the difference between the force of gravity (which pulls down) and the air resistance (which opposes the motion). The force of gravity can be calculated using the equation:
Force of gravity = mass (m) x acceleration due to gravity (g)
Here, the acceleration due to gravity is approximately 9.8 m/s^2.
Now, let's set up equations to solve for the mass:
Net force = Force of gravity - Air resistance
400 N = (m x 9.8 m/s^2) - (m x 4.5 m/s^2)
Rearranging the equation, we get:
(m x 9.8 m/s^2) - (m x 4.5 m/s^2) = 400 N
Next, we can combine the terms containing the mass:
9.8 m/s^2 - 4.5 m/s^2 = 400 N / m
Simplifying further:
5.3 m/s^2 = 400 N / m
Now, we can isolate the mass (m) by multiplying both sides of the equation by m:
5.3 m/s^2 x m = 400 N
Simplifying:
5.3 m = 400 N
Finally, we can solve for m:
m = 400 N / 5.3 m/s^2
m ≈ 75.47 kg
So, the mass of the paratrooper is approximately 75.47 kilograms.