A 75 kg skydiver in free fall is subjected to a crosswind exerting a force of
60 N and to a vertical air resistance force of 100 N. Calculate the resultant
force acting on the skydiver [6 marks] and his angle of fall (relative to
vertical) [6 marks].
Thee forces act on the skydiver:
Weight = M g = 735 N down
Vertical air resistance = 100 N up
(Net vertical force = 635 N down)
Horizontal wind force = 60 N
Resultant force = sqrt[(635^2 + 60^2] = 637.8 N
Ultimately, the skydiver will fall in the direction of the resultant force, arctan(60/635) = 5.4 degrees from vertical
Well, well, well, it seems like our skydiver is in quite a predicament! Let's calculate the resultant force on him and the angle of his fall.
To find the resultant force, we need to break down the forces into their horizontal and vertical components.
The horizontal component is the crosswind force, which is 60 N in this case. Since the skydiver is in free fall, there is no other force acting horizontally, so the horizontal component remains the same at 60 N.
Now, for the vertical component, we have the vertical air resistance force, which is 100 N. Since the skydiver is falling freely, we also have the force of gravity acting downwards, which is the product of his mass (75 kg) and the acceleration due to gravity (9.8 m/s^2). So, the force of gravity is 75 kg * 9.8 m/s^2 = 735 N.
To calculate the resultant force, we need to add the vertical components of the forces. The net vertical force is 100 N (vertical air resistance) - 735 N (force of gravity) = -635 N.
Now, we can use the Pythagorean theorem to calculate the magnitude of the resultant force. The magnitude of the resultant force is the square root of the sum of the squares of the horizontal and vertical components. In this case, it's the square root of (60 N)^2 + (-635 N)^2. Crunching the numbers, we get approximately 643.15 N.
Next, let's move on to calculating the angle of fall. We can use the formula: angle = arctan(vertical component / horizontal component). Plugging in the values, we get angle = arctan(-635 N / 60 N) ≈ -86.32 degrees.
Well, the resultant force is approximately 643.15 N (a rather strong force, I must say) and our skydiver is falling at an angle of approximately -86.32 degrees relative to vertical. That's quite the sideways descent! I hope he has a good sense of humor to make his fall a bit more enjoyable!
To calculate the resultant force acting on the skydiver, we need to consider the forces acting on the skydiver in the horizontal and vertical directions separately.
Horizontal Forces:
The only horizontal force acting on the skydiver is the crosswind force, which is 60 N.
Vertical Forces:
The skydiver is subjected to two vertical forces - the weight and the air resistance. The weight is given by the formula W = mg, where m is the mass of the skydiver and g is the acceleration due to gravity (approximately 9.8 m/s^2). So, the weight of the skydiver is W = 75 kg * 9.8 m/s^2 = 735 N. The air resistance force is given as 100 N.
To find the resultant force, we need to calculate the net force in the horizontal and vertical directions using the Pythagorean theorem.
Horizontal Net Force = Crosswind Force = 60 N
Vertical Net Force = Weight - Air Resistance = 735 N - 100 N = 635 N
To find the magnitude of the resultant force, we use the Pythagorean theorem:
Resultant Force = √(Horizontal Net Force^2 + Vertical Net Force^2)
Resultant Force = √(60^2 + 635^2) = √(3600 + 403225) = √407825 = 638.53 N
To find the angle of fall relative to vertical, we can use the inverse tangent function:
Angle = arctan(Vertical Net Force / Horizontal Net Force)
Angle = arctan(635 N / 60 N)
Angle = arctan(10.583)
Angle = 81.13 degrees (rounded to two decimal places)
Therefore, the resultant force acting on the skydiver is approximately 638.53 N, and the angle of fall relative to vertical is approximately 81.13 degrees.
To calculate the resultant force acting on the skydiver, we need to consider both the crosswind force and the vertical air resistance force. The crosswind force acts horizontally, while the vertical air resistance force acts vertically.
Resultant Force:
To find the resultant force, we can break down the forces into their horizontal and vertical components. Since the crosswind force is horizontal, its entire magnitude will contribute to the horizontal component. Thus, the horizontal component of the resultant force (F_hor) is 60 N.
The vertical air resistance force (F_air) opposes the downward force of gravity, so we subtract its magnitude from the force of gravity acting on the skydiver. The force of gravity can be calculated using the formula F_gravity = m * g, where m is the mass of the skydiver and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_gravity = 75 kg * 9.8 m/s^2 = 735 N
F_air = 100 N
Next, we subtract the vertical air resistance force from the force of gravity to find the vertical component of the resultant force (F_vert).
F_vert = F_gravity - F_air
= 735 N - 100 N
= 635 N
Now, we can calculate the magnitude of the resultant force (F_resultant) using the Pythagorean theorem:
F_resultant = √(F_hor^2 + F_vert^2)
= √(60^2 + 635^2)
≈ 636.20 N
Therefore, the resultant force acting on the skydiver is approximately 636.20 N.
Angle of Fall:
To find the angle of fall, we can use trigonometry. The angle of fall is the arctangent of the horizontal and vertical components of the resultant force.
tan(angle) = F_hor / F_vert
angle = arctan(F_hor / F_vert)
= arctan(60 N / 635 N)
≈ 5.34 degrees
Therefore, the angle of fall (relative to vertical) is approximately 5.34 degrees.