Terminal speed is the maximum speed that a falling object can reach and is based on aerodynamic resistance. In a vacuum, an object falling toward a planet as a result of gravity will continue to accelerate until it hits the ground.
However, if the object is falling through an atmosphere, such as on earth, then it will accelerate up to the point that the aerodynamic resistance cancels the downward force due to gravity, and it travels at a constant maximum speed, called the terminal velocity. At this point, resistance is equal to acceleration due to gravity. At terminal velocity, the skydiver's acceleration is zero.
Use the conservation of angular momentum; angular momentum at the beginning = angular momentum at the end
Conservation of angular momentum:
I1 w1 = I2 w2
Where I is the moment of inertia. For a sphere, I=2/5 m R^2. Substituting into the equation above we get
w2 = I1 w1 / I2 = w1 m1 R1^2 / (m2 R2^2)
w2 = w1 4 * (R1/R2)^2
= 4*(1)*(7E5/7.5)^2
= 3.48E10 revs/(17days)
= 2.04705882 x 10^9 revs/sec
Answer: 7.78m/s
Explanation: As the the skier slide down the height, we assume the motion of a body, slidind down an incline plane.
Force down the plane= [email protected]
Frictional force= umg
u= coefficient of friction
Net force on skier = [email protected] umg
ma = [email protected]
a = g([email protected] - u) = 9.8 (sin 25- 0.2)
a = 9.8 × (0.4226-0.2) = 9.8 × 0.2226
a = 2.18m/s²
Using the formula V² = U² + 2aH
Where H = (10.4+ 3.5)=total height of descent before landing, U= 0.
V = √ 2 × 2.18× 13.9 = √60.604
V = 7.78m/s
1) Data:
Vo = 20 m/s
α = 37°
Yo = 0
Y = 3m
2) Questions: V at Y = 3m and X at Y = 3 m
3) Calculate components of the initial velocity
Vox = Vo * cos(37°) = 15.97 m/s
Voy = Vo * sin(37°) = 12.04 m/s
4) Formulas
Vx = constant = 15.97 m/s
X = Vx * t
Vy = Voy - g*t
Y = Yo + Voy * t - g (t^2) / 2
5) Calculate t when Y = 3m (first time)
Use g ≈ 9.8 m/s^2
3 = 12.04 * t - 4.9 t^2
=> 4.9 t^2 - 12.04t + 3 = 0
Use the quadratic equation to solve the equation
=> t = 0.28 s and t = 2.18s
First time => t = 0.28 s.
6) Calculate Vy when t = 0.28 s
Vy = 12.04 m/s - 9.8 * 0.28s = 9.3 m/s
7) Calculate V:
V = √ [ (Vx)^2 + (Vy)^2 ] = √[ (15.97m/s)^2 + (9.30 m/s)^2 ] = 18.48 m/s
tan(β) = Vy/Vx = 9.30 / 15.97 ≈ 0.582 => β ≈ arctan(0.582) ≈ 30°
Answer: V ≈ 18.5 m/s, with angle ≈ 30°
8) Calculate X at t = 0.28s
X = Vx * t = 15.97 m/s * 0.28s = 4,47m ≈ 4,5m
Answer: X ≈ 4,5 m
