A firefighter who weighs 192 lb slides down an infinitely long fire pole that exerts a frictional resistive force with magnitude proportional to her speed with constant of proportionality k. Find her velocity v as a function of t, given that her terminal velocity is -16 ft/s. Assume that she starts from rest. Solve for the solution of this Application of first order differential equation in Dynamics. the final answer is v= -16 (1-e-2t)

Problem 4

>V=0 d (m A block of mass m is on an inclined ramp. The ramp makes an angle with respect to the horizontal, as shown. The ramp has friction, with coefficient of kinetic friction and static friction μs. This experiment takes place on earth. The block has an initial speed of v up the ramp. It travels a distance d along the ramp before it stops. There are no numbers in this problem! Answer all questions in terms of the given variables (g, m, µk, µs, 8, v, d) only. Do not use any other variables. a) Draw a free body diagram clearly showing all the forces acting on the block while it is moving up the ramp. b) Calculate the work done by the Normal force as the block travels the distance d. Is it positive, negative, or zero? c) Calculate the work done by the Weight force as the block travels the distance d. Is it positive, negative, or zero? d) Calculate the work done by the Friction force as the block travels the distance d. Is it positive, negative, or zero? e) If the block comes to rest,…

A parachutist whose mass is 60 kg drops from a helicopter hovering 1000 m above the ground and falls toward the ground under the influence of gravity. Assume that the force due to air resistance is proportional to the velocity of the parachutist, with the proportionality constant b₁ = 20 N-sec/m when the chute is closed and b2 = 90 N-sec/m when the chute is open. If the chute does not open until the velocity of the parachutist reaches 25 m/sec, after how many seconds will the parachutist reach the ground? Assume that the acceleration due to gravity is 9.81 m/sec². The parachutist will reach the ground after (Round to two decimal places as needed.) seconds.

A 40 kg wooden crate is being pulled across a wooden surface by a force (of magnitude F) that is angled 20° above the horizontal. The coefficient of static friction is 0.5 and the coefficient of kinetic friction is 0.3. (a)Calculāte the minimum force F (in N) that must be exerted to get the crate moving. (b)What is the acceleration (in m/s?) of the crate once it starts to move, if that force (F) is maintained?

An object undergoes one-dimensional motion along the x-axis subject to the the decelerating force dv kæv² m dt At time t = 0, the object's position is x = 0 and its velocity is v = v0. The decelerating force is a dv dv dx function of the object's position x(t) and velocity v(t). Using the fact that dt transform the dx dt problem into one having x as the independent variable. Solve for v as a function of x and v0 then determine the position xf at which the object comes to rest. If the object does not come to rest then xf = 00 (enter oo for infinity) dv = V = Xf = Question Help: O Message instructor Submit Question

Consider a speherical speck of dust of mas 1.5*10^-11 kg and radius 2.1*10^-6m with drag coefficient CD= 0.5 falling in air with density P(air) = 1.2kg/m^3. What is the terminal velocity of the dust? Area= pie*r^2

An object of mass m falls from rest under gravity subject to an air resistance proportional to its speed. Taking the y axis as positive down, show that the differential equation of motion is m(dv/dt) = mg − kv, where k is a positive constant. Find v as a function of t, and find the limiting value of v as t tends to infinity; this limit is called the terminal speed. Can you find the terminal speed directly from the differential equation without solving it? Hint: What is dv/dt after v has reached an essentially constant value? Consider the following specific examples of this problem.(a) A person drops from an airplane with a parachute. Find a reasonable value of k.(b) In the Millikan oil drop experiment to measure the charge of an electron, tiny electrically charged drops of oil fall through air under gravity or rise under the combination of gravity and an electric field. Measurements can be made only after they have reached terminal speed. Find a formula for the time required for a drop…

A speedboat is cruising at a speed of 11.8 m/s in still water when it shuts off its engines and coasts to rest. The water exerts drag forces on the speedboat such that its speed during coasting is given by v = v₁e-ct, where v is the speed at time t, v, is the initial speed at t = 0, and c is a constant. At a time of t = 19.5 s after the engines are cut, the speed is 5.00 m/s. (a) What is the constant c (in s-¹) in the expression? -1 (b) What is the speed (in m/s) at t = 40.0 s? m/s (c) Given the expression above for the speed at any time, which of the expressions below gives the speedboat's acceleration while coasting? O OO a = -cv a = CV i a = -ce a = ce S a = cv -ct -ct

A skydiver with mass 75 kg jumps out of an airplane that is 5 km above the ground. Aside from gravity (assume constant -9.8 m/s^2) the only force on the skydiver is air resistance, which we will assume is kv in the direction opposing motion. The conventional wisdom is that terminal velocity for a skydiver is 55 meters per second. If that's true for our skydiving friend, then what is the value of k? Enter your answer rounded to the two decimal places.