A parachutist jumps out of airplane with an initial speed of 2.0 m/s downwards. There is a force of air resistance

equivalent to 305 N. Determine the parachutist’s mass if it takes a total of 3 seconds for him to travel 30 m
downwards.

To determine the parachutist's mass, we can use the equation:

Force of gravity - Force of air resistance = mass × acceleration

The force of gravity is equal to the weight of the parachutist, which can be calculated using the formula:

Force of gravity = mass × gravitational acceleration

Since the parachutist is traveling downwards, the net force acting on the parachutist is:

Net force = Force of gravity - Force of air resistance

The acceleration of the parachutist can be calculated using the equation:

Acceleration = (final velocity - initial velocity) / time

In this case, the initial velocity is 2.0 m/s downwards, the final velocity is 0 m/s (since the parachutist reaches a constant speed), and the time is 3 seconds. So, the acceleration is:

Acceleration = (0 - (-2.0)) / 3

Now, let's substitute the values into the equation for the net force:

Net force = mass × acceleration

(Force of gravity - Force of air resistance) = mass × acceleration

Since we know that the force of air resistance is 305 N and the acceleration is calculated as above, we can rearrange the equation to solve for mass:

mass = (Force of gravity - Force of air resistance) / acceleration

Let's calculate:

mass = (weight - 305 N) / acceleration

Now, we need to calculate the weight:

weight = mass × gravitational acceleration

Let's substitute the values into the formulas:

weight = mass × gravitational acceleration

mass = (weight - 305 N) / acceleration

mass × gravitational acceleration = (mass × gravitational acceleration - 305 N) / acceleration

mass × gravitational acceleration - mass × gravitational acceleration = - 305 N / acceleration

mass × (gravitational acceleration - gravitational acceleration) = - 305 N / acceleration

mass × 0 = -305 N / acceleration

mass = -305 N / 0

Since division by zero is undefined, we cannot determine the parachutist's mass with the given information. Please double-check the values and equations used.

To determine the parachutist's mass, we need to use the equations of motion that relate distance, time, initial velocity, final velocity, acceleration, and force.

We know that the initial velocity is 2.0 m/s downwards, and the distance traveled is 30 m downwards. The time it takes to travel this distance is 3 seconds.

First, let's find the final velocity using the equation of motion:

v = u + at

where:
v = final velocity
u = initial velocity
a = acceleration
t = time

In this case, the final velocity is unknown, the initial velocity is 2.0 m/s downwards, the acceleration is due to air resistance, and the time is 3 seconds.

Since the force of air resistance is equivalent to 305 N, we can use Newton's second law of motion to determine the acceleration:

F = ma

where:
F = force
m = mass
a = acceleration

In this case, the force of air resistance is 305 N, and the mass is unknown.

Now, rearranging the equation:

a = F / m

we can substitute the given values to find the acceleration.

Next, we can substitute the values of initial velocity, time, and acceleration into the equation of motion to find the final velocity.

Finally, we can use the equations of motion again to find the parachutist's mass.

Let's calculate step-by-step:

Step 1: Calculate acceleration
a = F / m

Given:
F = 305 N (force of air resistance)
a = acceleration
m = unknown (mass)

a = 305 N / m

Step 2: Calculate final velocity
v = u + at

Given:
v = final velocity (unknown)
u = 2.0 m/s downwards (initial velocity)
a = acceleration (from step 1)
t = 3 seconds (time)

v = 2.0 m/s + a * 3 s

Step 3: Calculate mass
Use the equation of motion:

v^2 = u^2 + 2as

where:
v = final velocity (from step 2)
u = 2.0 m/s (initial velocity)
a = acceleration (from step 1)
s = 30 m (distance traveled)

(v^2 - u^2) / 2 = as

Step 4: Substitute the values and solve for mass
((2.0 m/s + (305 N / m * 3 s))^2 - (2.0 m/s)^2) / 2 = (305 N / m)(30 m)

Simplify the equation and solve for m.