# What is Terminal speed: Definition and 30 Discussions

Terminal velocity is the maximum velocity (speed) attainable by an object as it falls through a fluid (air is the most common example). It occurs when the sum of the drag force (Fd) and the buoyancy is equal to the downward force of gravity (FG) acting on the object. Since the net force on the object is zero, the object has zero acceleration.In fluid dynamics, an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving.As the speed of an object increases, so does the drag force acting on it, which also depends on the substance it is passing through (for example air or water). At some speed, the drag or force of resistance will equal the gravitational pull on the object (buoyancy is considered below). At this point the object stops accelerating and continues falling at a constant speed called the terminal velocity (also called settling velocity). An object moving downward faster than the terminal velocity (for example because it was thrown downwards, it fell from a thinner part of the atmosphere, or it changed shape) will slow down until it reaches the terminal velocity. Drag depends on the projected area, here, the object's cross-section or silhouette in a horizontal plane. An object with a large projected area relative to its mass, such as a parachute, has a lower terminal velocity than one with a small projected area relative to its mass, such as a dart. In general, for the same shape and material, the terminal velocity of an object increases with size. This is because the downward force (weight) is proportional to the cube of the linear dimension, but the air resistance is approximately proportional to the cross-section area which increases only as the square of the linear dimension. For very small objects such as dust and mist, the terminal velocity is easily overcome by convection currents which prevent them from reaching the ground and hence they stay suspended in the air for indefinite periods. Air pollution and fog are examples of convection currents.

View More On Wikipedia.org
1. ### Terminal Speed of Vessel in Vacuum and Weightlessness

In vacuum and weightlessness, at the bottom of a cylindrical vessel (a cup), there is a layer of solid substance of molar mass μ. This substance sublimes slowly (evaporates from the solid phase into gaseous phase) and pushes thereby the vessel to the opposite direction. Estimate the terminal...
2. ### Show that the terminal speed of a falling spherical object ....

To write ##v## as a function of time, I wrote the equation ##m\frac{dv}{dt} = c_{2}v^2 + c_{1}v - mg \implies \frac{mdv}{c_{2}v^2 + c_{1}v - mg} = dt## To solve this, I thought about partial fractions, but several factors of ##-c_{1} \pm \sqrt {c_{1}^2 +4c_{2}*mg}## would appear and they don't...
3. ### How do I find the terminal speed of a body in water?

Homework Statement A baseball has a terminal speed of 42 m/s in air (ρ = 1.2 kg/m^3). What would be its terminal speed in water (ρ = 1.0 x 10^3 kg/m^3)? A) 0.05 m/s B) 1.5 m/s C) 18 m/s D) 42 m/s E) 1200 m/s Homework Equations D=½Cρ*Av^2 where the magnitude of the drag force (D), relative...
4. ### Thermal velocity of a soccer ball

Hello, I am an IB HL Physics student. I am thinking of doing my IA on the thermal velocity of a soccer ball. I will be using a soccer ball shooter (machine) to simulate the thermal velocity. I have a couple of questions: what is the thermal velocity equation, which would fit for a soccer...
5. ### Falling object in a gravitational field with v^2 drag force

Homework Statement Consider a particle in a gravitational field that is also subject to a resisting force proportional to the velocity squared ( Fdrag = + or - cv2). a) Find the terminal velocity, vT, for the object as it falls. b) Show that for an object dropped from rest that the velocity...
6. ### Calculate terminal velocity when given cross sectional area

Homework Statement Two packages are dropped from an airplane. A parachute can increase the cross sectional area of each packages by a factor of 31. The parachute on package 1 fails to open, and the terminal speed of package 1 is 10 m/s. The parachute on package 2 opens. What is the terminal...
7. ### Calculating Terminal Speed of a 82kg Skydiver using Basic Physics Formulas

Homework Statement A 82kg skydiver can be modeled as a rectangular "box" with dimensions 21cm× 44cm× 1.8m Homework Equations v = sqrt(2mg/(rho * C *A)) The Attempt at a Solution A = 0.21 m * 0.44 m = 0.0924 m^2 v = sqrt(2 * 82 kg * 9.81 m/s^2 / (1.2 kg/m^2 * 0.0924 m^2 * 0.80))...
8. ### Terminal speed with linear drag

Homework Statement An object moves through a liquid horizontally against a linear drag force given by F = -cv What is the terminal velocity? Initial Velocity is V_0 Homework Equations F=ma The Attempt at a Solution m(dv/dt) = -cv --> (dv/v) = (-c/m)dt ln(vf/v0) = -ct/m...
9. ### What is the expression for terminal speed in this homework statement?

Homework Statement Homework Equations That is the solution: The Attempt at a Solution I think ε≠Bvl because ε = - dø/dt=- Bd(v.t)/dt, v is not constant. Why ε=Bvl?
10. ### Kinematics - Velocity, force of gravity, terminal speed

Hi everyone, I would really appreciate any advice on how to go about solving the following problem. I'm supposed to investigate it in a report. Homework Statement A paratrooper who jumps out of an aircraft moving in horizontal flight initially has the same horizontal velocity as the aircraft...
11. ### Terminal Speed for Skier Going Down Slope

Homework Statement What is the terminal speed for an 75.0kg skier going down a 35.0∘ snow-covered slope on wooden skis μk= 0.060? Assume that the skier is 1.60m tall and 0.300m wide. Express your answer using two significant figures with the appropriate units. Area skier = A =...
12. ### Terminal speed. Calculus. Time.

Homework Statement An object of mass m falls from rest subject to air resistance force directly proportional to the object's speed, F=-bv, where b is the proportionality constant in N/(m/s) and the negative sign indicates the direction of the force opposite to the direction of the velocity...
13. ### Terminal Speed in Projectile Motion under Air Resistance

Homework Statement Terminal speed = 43 m s-1Homework Equations Acceleration in y direction when ball falling down: ay = - g + \alphavvy where \alpha = K/m and v = (vx2 + vy2)^0.5The Attempt at a Solution Putting ay = 0 as there is no acceleration when terminal speed occurs. However, is vvy...
14. ### Compute the terminal speed of a car as it coasts down the incline

Homework Statement A Toyota Prius has a total mass of 1520 kg when carrying passengers. The driver shifts the car into neutral and coasts down a long, straight section of road with a grade of 9% (the term "grade" means slope). The car eventually reaches a terminal speed. Ignoring the effects of...
15. ### Estimate the terminal speed of a wooden sphere

Homework Statement (a) Estimate the terminal speed of a wooden sphere (density 0.870 g/cm3) falling through air, if its radius is 8.50 cm and its drag coefficient is 0.500. (The density of air is 1.20 kg/m3.) (b) From what height would a freely falling object reach this speed in the absence...
16. ### Question about terminal speed using drag

What is the terminal speed of a 75 kg man that jumps out of a plane feet first? The man can be thought of as a rectangular box with dimensions 20 cm * 40 cm * 1.8 m I tried equation v terminal = sq rt (4mg/p* area). P=1.22 I used . 72 as Area. That's wrong. Help please! I calculated...
17. ### What is the drag force on a missile at low altitude?

Homework Statement Missile Calculate the drag force on a missile 48 cm in diameter cruising with a speed of 270 m/s at low altitude, where the density of air is 1.2 kg/m3. Assume C = 0.75. Homework Equations Fd = -1/2p(v^2)CA The Attempt at a Solution...
18. ### What Determines the Terminal Speed of a Skier?

Homework Statement What is the terminal speed for an 85.0 kg skier going down a 44 degree snow-covered slope on wooden skis μ= 0.060? Assume the skier is 1.7m tall and .50m wideHomework Equations v = sqrt(4μmg/A) The Attempt at a Solution The area of the skier is (1.7m*.5m)=0.85m^2 sqrt...
19. ### What is the Y-Component of a Baseball's Acceleration at Half Its Terminal Speed?

Homework Statement A baseball is thrown straight up. The drag force is proportional to v^2. In terms of g , what is the y-component of the ball's acceleration when its speed is half its terminal speed and it is moving up? moving back down? Homework Equations F=ma mg+bv^2=ma mg-Bv^2=ma The...
20. ### Terminal speed and acceleration problem

I'm having trouble figuring this one out. Hope someone can help A ball dropped from rest accelerates at a rate of 9.81 m/s2 if we ignore air resistance. If air resistance is not ignored, the ball reaches a terminal speed when the friction force of the air acting on the falling ball is...
21. ### Determining the time it takes to reach half of a penny's terminal speed

The question is: The terminal speed of a penny is 11 m/s. By neglecting air resistance, calculate how long it takes for a penny falling from rest to reach half of this speed Homework Equations I thought maybe you had to use one of the kinematic equations but that didnt work The...
22. ### Terminal Speed and Height of Object

Homework Statement (a) Calculate the terminal speed of a wooden sphere(density .830 g/cm^3) falling through the air if its radius is 8.00cm and its drag coefficient is .500. (b) From what height would a freely falling object reach this speed in the absence of air resistance? Homework...
23. ### How Does Mass Affect the Terminal Speed of Falling Objects?

one way to determine how the terminal speed depends on the mass of an object is to observe the motion of flat-bottomed coffee filters falling vertically toward a motion sensor. My teacher told me we will do 3 sets of test. first one is with 1 filter, second with 2 stacked filters, and 3rd one...
24. ### What is the terminal speed of the paratrooper?

Homework Statement A helicopter drops a paratrooper carrying a siren that emits a 788 Hz audible signal. The microphone (reciever) on the plane monitors the signal from the transmitter as the paratrooper falls. Take the speed of sound in air to be 343 m/s and assume the paratroopers always...
25. ### Acceleration and terminal speed problem

Homework Statement A small piece of Styrofoam packing material is dropped from a height of 2.10 m above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by a = g - bv. After falling 0.400 m, the styrofoam effectively reaches its terminal speed, and then...
26. ### Terminal speed and forces question

A 72.0 kg skydiver can be modeled as a rectangular "box" with dimensions 24.0 cm\times 47.0 cm\times 178 cm. All I know is drag is a force so F=m*a or d=m*g which is 705.6N. After this I have no idea what to do. Any help?
27. ### Problems with acceleration due to gravity, and terminal speed

My first question: 1. A baseball pitcher throws a ball vertically upward and catches it at the same level 4.2s later. a) With what velocity did the pitcher throw the ball? b) How high did the ball rise? (my work, which is wrong according to the book) a) v_2 = v_1 + (a)\Delta(t)...
28. ### Find the terminal speed of a 750-kg rocket

Find the terminal speed of a 750-kg rocket that starts from rest carrying 2600kg of fuel and that expels its exhuast gases at 1.8 k/ma here's the formula I am using: v_f = v_i + v_{ex}*ln{\frac{M_i}{M_f}} well since it's at rest, initial velocity is zero. so... v_f = 1.8*ln(750/2500)...
29. ### Terminal Speed of Golf Ball Dropped from 25m

will a golf ball of mass 45g and diamter 4.3cm reach terminal speed when dropped from a height of 25m? the drag coefficient is 0.35 and the density of air is 1.2kg/m^3. using the formula v_t = sqrt(\frac{2*mg}{CpA}) v_t = sqrt(\frac{2*(45g)(9.8m/s^2)}{(.35)(1.2kg/m^3)(0.043m)}) so...
30. ### Terminal Speed of 6.5 kg Ball: Calc Error?

What is the terminal speed of a 6.5 kg spherical ball with a radius of 3.0 cm and a drag coefficient of 1.50? The density of the air through which the ball falls is 1.2 kg/m3. I used vt=sqrt((2Fg)/(CpA)). Where Fg is force of gravity, C is drag coeff., p is air density , and A is cross...