At about 51.2 meters/sec, a falling parachuter (before the parachute opens) no longer accelerates. Air friction opposes acceleration. Although the effect of air friction begins gradually, imagine that the parachuter is free falling until terminal velocity (the constant falling speed where the pull of gravity is cancelled out by air resistance) is reached.
How long would that take?
vf=vi+at vi=0 vf=51.2m/s, a= 9.8 solve for t.
To calculate the time it takes for the parachuter to reach terminal velocity, we can use the following formula:
t = (v - u) / a
where:
t = time taken
v = final velocity (terminal velocity)
u = initial velocity
a = acceleration
In this case, the initial velocity is 0 m/s (since the parachuter is free falling), the final velocity is 51.2 m/s, and the acceleration is the force of gravity acting on the parachuter, which is approximately 9.8 m/s².
Plugging in these values, the formula becomes:
t = (51.2 - 0) / 9.8
Simplifying the equation, we get:
t ≈ 5.224 seconds
Therefore, it would take approximately 5.224 seconds for the parachuter to reach terminal velocity.
To calculate the time it takes for a parachutist to reach terminal velocity, you need to use the concept of acceleration due to gravity and air resistance. Terminal velocity is the point at which the force of gravity pulling the parachutist downwards is equal to the force of air resistance pushing upward, resulting in a net force of zero.
Here's how you can calculate the time it takes for a parachutist to reach terminal velocity:
1. Determine the gravitational acceleration: The acceleration due to gravity is typically represented as "g" and is approximately 9.8 meters per second squared (m/s^2).
2. Use the formula for net force: The net force acting on the parachutist is given by the difference between the force of gravity and the force of air resistance. At terminal velocity, these forces cancel each other out, so the net force is zero.
3. Equate the forces: Set the force of gravity equal to the force of air resistance:
Force of Gravity = Force of Air Resistance
m * g = k * v
where m is the mass of the parachutist, g is the gravitational acceleration, k is a constant representing air resistance, and v is the velocity of the parachutist.
4. Solve for velocity: Rearrange the equation to solve for velocity, v:
v = m * g / k
5. Substitute values: Plug in the values you have. You know the velocity at which the parachutist stops accelerating is 51.2 m/s, so the equation becomes:
51.2 = m * 9.8 / k
6. Solve for k: Rearrange the equation to solve for k:
k = m * 9.8 / 51.2
7. Use known values for m and g: Assuming the mass of the parachutist is 75 kg, plug in the values:
k = 75 * 9.8 / 51.2
This gives you the value of k, which represents air resistance.
8. Calculate the time: Use the formula for velocity, where initial velocity is 0, final velocity is the terminal velocity, and time is unknown:
v = u + a * t
where u is the initial velocity, a is the acceleration, and t is time. Since there is no initial velocity and the acceleration is constant (0), the formula simplifies to:
v = a * t
Substitute the terminal velocity for v and solve for time:
51.2 = 0 * t
Since the time is zero, the parachutist reaches terminal velocity instantaneously.
Therefore, it would take an infinitesimally small amount of time (essentially zero time) for the parachutist to reach terminal velocity.