A skydiver jumps out of an airplane and falls freely until reaching terminal velocity. Calculate the terminal velocity of the skydiver based on their mass and the drag coefficient.
Guide On Rating System
Vote
To calculate the terminal velocity of the skydiver, we need to consider the forces acting on the skydiver during free fall.
The two main forces acting on the skydiver are gravity and air resistance.
1. Gravity: The force due to gravity is given by the equation Fg = mg, where Fg is the gravitational force, m is the mass of the skydiver, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Air Resistance: The force due to air resistance is given by the equation Fa = 0.5 * ρ * v^2 * A * Cd, where Fa is the air resistance force, ρ is the density of air (approximately 1.225 kg/m^3), v is the velocity of the skydiver, A is the cross-sectional area presented by the skydiver, and Cd is the drag coefficient.
At terminal velocity, the air resistance force equals the gravitational force, so we can set Fa = Fg.
0.5 * ρ * v^2 * A * Cd = mg
Rearranging the equation to solve for velocity (v):
v = sqrt(2 * mg / (ρ * A * Cd))
The terminal velocity of the skydiver can be calculated using the above equation, given their mass (m) and the drag coefficient (Cd). The specific cross-sectional area (A) needs to be provided for an accurate calculation.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99