A skydiver with a weight of 185 lbs is falling. At a certain moment the force of air resistance on the sky diver is 145 lbs. What is the skydiver's acceleration at this moment? (Hint: Remember that the weight of an object is given by mg.)
AND When the skydiver reaches a terminal velocity, what will be the new force of air resistance?
To find the skydiver's acceleration at a certain moment, we need to consider the net force acting on the skydiver. In this case, the force of air resistance is opposing the force of gravity (weight).
1. Calculate the force of gravity (weight):
The weight is given by the formula weight = mass * gravity. The mass of the skydiver is not provided, but we can find it using the same formula.
Assuming g = 32 ft/s^2 (typical gravity on Earth):
Weight = 185 lbs
Mass = Weight / gravity = 185 lbs / 32 ft/s^2 = 5.78 slugs (1 slug = 32.2 lbs)
2. Determine the net force:
The net force is the difference between the force of air resistance and the force of gravity.
Net Force = Force of air resistance - Force of gravity
= 145 lbs - 185 lbs
= -40 lbs (Note: The negative sign indicates that the force of air resistance is acting in the opposite direction to the force of gravity)
3. Calculate acceleration:
Using Newton's second law (F = ma), we can solve for acceleration.
Net Force = mass * acceleration
-40 lbs = 5.78 slugs * acceleration
acceleration = -6.91 ft/s^2 (Note: The negative sign indicates that the acceleration is in the opposite direction to the force of gravity)
Therefore, the skydiver's acceleration at this moment is approximately -6.91 ft/s^2.
Now, let's move on to the second part of the question about terminal velocity.
Terminal velocity is the maximum velocity at which an object in freefall can no longer accelerate. At this point, the force of air resistance is equal to the force of gravity, resulting in a net force of zero.
4. At terminal velocity, the new force of air resistance is equal to the force of gravity:
Force of air resistance = Force of gravity
Therefore, the new force of air resistance is 185 lbs.
Hence, when the skydiver reaches terminal velocity, the force of air resistance will be 185 lbs.