a 75 kg person escapes from a burning building by jumping from a window 30 m above a catching net. Acceleration due to gravity is 9.81 m/s^2. Assuming air resistance is simply a constant 96 N force on the person during the fall, determine the person's velocity just before hitting the net. answer in m/s.
so Fg = 75*9.81 = 735.75 N
Fnet = ma
Fair - Fg = ma
96 - 735.75 = 75 * a
a = -8.53 m/s2
Vf2 = Vo2 +2ax
Vf2 = 0 + 2(-8.53)(-30)
Vf2 = 511.8
Vf = -22.63 m/s //neg b/c downward direction
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Well, well, well! Looks like someone has a hot question about a burning building. Let's dive right into it!
To find the person's velocity just before hitting the net, we need to consider a few things. First, we'll calculate the person's acceleration during the fall, taking into account both gravity and the air resistance force.
The net force acting on the person is the force due to gravity minus the air resistance force. So, we have:
Net Force = Force due to gravity - Air resistance force
Net Force = (mass x acceleration due to gravity) - Air resistance force
Net Force = (75 kg x 9.81 m/s^2) - 96 N
Net Force = 738.75 N - 96 N
Net Force = 642.75 N
Now, we can use Newton's second law of motion, which states that force equals mass times acceleration:
Force = mass x acceleration
642.75 N = 75 kg x acceleration
Solving for acceleration, we get:
acceleration = 642.75 N / 75 kg
acceleration ≈ 8.57 m/s^2
Since the person is falling vertically downward, we only need to consider the vertical component of their velocity. By using the equation:
final velocity^2 = initial velocity^2 + 2 x acceleration x distance
We can find the final velocity just before hitting the net. The initial velocity is zero because the person starts from rest.
0^2 + 2 x 8.57 m/s^2 x 30 m = final velocity^2
0 + 514.2 m^2/s^2 = final velocity^2
final velocity^2 = 514.2 m^2/s^2
Taking the square root of both sides, we get:
final velocity ≈ 22.7 m/s
So, the person's velocity just before hitting the net would be approximately 22.7 m/s. But remember, this calculation doesn't account for factors such as air resistance changing with velocity or the net's ability to provide additional resistance. Safety first, my friend!
To determine the person's velocity just before hitting the net, we can use the equations of motion.
First, let's determine the net force acting on the person during the fall. The force due to gravity can be calculated as the product of the person's mass (75 kg) and the acceleration due to gravity (9.81 m/s^2), which gives:
Force due to gravity = (75 kg) * (9.81 m/s^2) = 735.75 N
Since air resistance is a constant 96 N force acting in the opposite direction, the net force becomes:
Net Force = Force due to gravity - Air Resistance = 735.75 N - 96 N = 639.75 N
Next, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Net Force = mass * acceleration
Since we want to find the velocity, we rearrange the equation to solve for acceleration:
acceleration = Net Force / mass
Plugging in the values:
acceleration = 639.75 N / 75 kg
Simplifying:
acceleration = 8.53 m/s^2
Now, we can use one of the equations of motion to find the final velocity of the person just before hitting the net. The equation we need is the following, where v is the final velocity, u is the initial velocity (which is 0 m/s since the person starts from rest), a is the acceleration, and s is the distance:
v^2 = u^2 + 2as
Plugging in the known values:
v^2 = 0^2 + 2 * 8.53 m/s^2 * 30 m
Simplifying:
v^2 = 2 * 8.53 m/s^2 * 30 m
v^2 = 511.8 m^2/s^2
Taking the square root of both sides to solve for v:
v = √(511.8 m^2/s^2)
v ≈ 22.65 m/s
Therefore, the person's velocity just before hitting the net is approximately 22.65 m/s.