Estimate the speed of the parachutist descending at the constant velocity with open parachute. Assume the area of the parachute, A = 30 m^2, mass of a person, m = 100 kg, and density of air, roh = 1 kg/m^3. Enter the answer limited to the second decimal place.
Hint 1: air pushing on the parachute exerts the resistive force which matches (equal and opposite) the gravitational force on the person. Hint 2: speed of the air striking the parachute is equal to the speed of the parachutist. Hint 3: force exerted by the air on parachute = (impulse exerted by air)/time interval during which the air strikes the parachute Hint 4: mass of air molecules striking the parachute can be found as mass of the air molecules in the cylinder of air below the parachute Hint 5: height of this cylinder = velocity of air multiplied by the time interval during which it is stopped by the parachute
* physics - drwls, Monday, February 21, 2011 at 12:07pm
I find the hints confusing. Here is the formula you need.
M*g = (1/2)*rho*A*Cd*V^2
Solve for the limiting velocity, V
*Cd is the dimensionless "drag coefficient", which is about 1.5 for a hemispherical parachute shape.
*rho is the density of air
*A is the projected area of the parachute (pi R^2), (not the surface area)
*g is the acceleration of gravity
* M is the mass
I answered it. Why are you posting it again?
To estimate the speed of the parachutist descending at a constant velocity with an open parachute, we can use the formula:
M*g = (1/2)*rho*A*Cd*V^2
where:
M = mass of the person (100 kg)
g = acceleration due to gravity (9.8 m/s^2)
rho = density of air (1 kg/m^3)
A = area of the parachute (30 m^2)
Cd = drag coefficient (approximately 1.5 for a hemispherical parachute shape)
V = velocity of the parachutist (desired answer)
First, rearrange the formula to solve for V:
V^2 = (2*M*g) / (rho*A*Cd)
Now, substitute the given values into the formula:
V^2 = (2 * 100 kg * 9.8 m/s^2) / (1 kg/m^3 * 30 m^2 * 1.5)
V^2 = 1960 / 45
V^2 ≈ 43.56
To get the speed, take the square root of both sides of the equation:
V ≈ √43.56
V ≈ 6.60 m/s
Therefore, the estimated speed of the parachutist descending at a constant velocity with an open parachute is approximately 6.60 m/s.