A paratrooper w/ a fully loaded pack has a mass of 120kg. The force due to air resistance on him when falling w/ an unopened parachute has magnitude
F(sub)d = bv^2, where b=0.14 N*s/m^2.
a) if he is falling w/ an unopened parachute at 64m/s, whats is the force of air resistance acting on him?
b) what is his acceleration?
c) what is his terminal velocity?
I figured that to be:
v(sub)t= sqrt (120 *9.8) / (0.14)
Can someone please help me find acceleration and the force of air resistance?
Thank you!! :)
a) Use the formula that was provided. The drag force is
F = b*(64)^2 = 573 N at v = 64 m/s
b) a = F/Mass
c) Let the terminal velocity be V. It occurs when bV^2 = M g. That is before the parachute opens.
V = sqrt (M g/b)
which is what you had
The value of b will increase by a large factor when the parachute opens, but the question is not concerned with that.
a) To find the force of air resistance acting on the paratrooper, we need to substitute the given values into the equation F(sub)d = bv^2.
F(sub)d = b * v^2
F(sub)d = 0.14 * (64)^2
Calculate the value:
F(sub)d = 576.96 N
So, the force of air resistance acting on the paratrooper when falling with an unopened parachute at 64 m/s is 576.96 N.
b) To find the acceleration, we can use Newton's second law of motion, which states that force is equal to mass times acceleration (F = ma). Rearranging the equation gives us a = F/m.
a = F(sub)d / m
a = 576.96 / 120
Calculate the value:
a = 4.808 m/s^2
So, the acceleration of the paratrooper is 4.808 m/s^2.
c) To find the terminal velocity, we need to set the force due to air resistance equal to the force due to gravity, as they balance each other out. So:
F(sub)d = mg
Substituting the given values into the equation:
bv^2 = mg
Rearranging the equation gives us:
v^2 = (mg) / b
Dividing both sides by the mass of the paratrooper:
v^2 / m = g / b
Substituting the values:
v^2 / 120 = 9.8 / 0.14
Calculate the value:
v^2 = 8348.57
Taking the square root of both sides:
v = √8348.57
Calculate the value:
v ≈ 91.42 m/s
Therefore, the terminal velocity of the paratrooper is approximately 91.42 m/s.
To find the force of air resistance acting on the paratrooper, we can use the equation F(sub)d = bv^2, where b = 0.14 N*s/m^2 and v = 64 m/s.
a) The force of air resistance can be calculated by plugging in the values into the equation:
F(sub)d = 0.14 * (64)^2
F(sub)d = 0.14 * 4096
F(sub)d = 573.44 N
Therefore, the force of air resistance acting on the paratrooper is 573.44 N.
b) To find the acceleration, we need to use Newton's second law: F = ma, where F is the net force acting on the paratrooper, m is the mass of the paratrooper, and a is the acceleration.
Since there are two forces acting on the paratrooper - the force of gravity (mg) and the force of air resistance (F(sub)d), the net force can be written as:
F(net) = F(sub)d - mg
Substituting the given values:
F(net) = 573.44 N - (120 kg * 9.8 m/s^2)
F(net) = 573.44 N - 1176 N
F(net) = -602.56 N
Since the net force is negative, it means the force of gravity is greater than the force of air resistance. Therefore, the acceleration will be in the upward direction (opposite to the direction of motion).
Using F = ma, we can rearrange the equation to solve for acceleration:
a = F(net) / m
a = -602.56 N / 120 kg
a = -5.021 m/s^2
Therefore, the acceleration of the paratrooper is approximately -5.021 m/s^2.
c) To find the terminal velocity, we need to equate the force of air resistance to the force of gravity (mg). At terminal velocity, the net force is zero (F(net) = 0), and the paratrooper stops accelerating.
Setting F(net) = 0:
F(sub)d - mg = 0
0.14v^2 - (120 kg * 9.8 m/s^2) = 0
Solving for v:
0.14v^2 = 1176
v^2 = 1176 / 0.14
v^2 = 8400
v = sqrt(8400)
v ≈ 91.65 m/s
Therefore, the terminal velocity of the paratrooper is approximately 91.65 m/s.