A man with a parachute jumps at a great height from an airplane moving horizontally. After 10 seconds, he opens his parachute. Find his velocity at the end of 15 seconds and his terminal velocity (i.e., the approximate velocity with which he will float to the ground). Assume that the combined weight of man and parachute is 160 pounds, and the force of the air resistance is proportional to the first power of the velocity, equaling 4v when the parachute is closed and 10v when it is opened

A man with a parachute jumps at a great height from an airplane moving horizontally. After 10 seconds, he opens his parachute. Find his velocity at the end of 15 seconds and his terminal velocity (i.e., the approximate velocity with which he will float to the ground). Assume that the combined weight of man and parachute is 160 pounds, and the force of the air resistance is proportional to the first power of the velocity, equaling 4v when the parachute is closed and 10v when it is opened

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A water balloon of mass 1000 grams is rolled on level ground with an initial velocity of 35 meters per second. As it travels, water leaks from the balloon at a rate of 140 grams per second. Assume air resistance is proportional to velocity with coefficient 94 grams per second. (a) Find the velocity of the balloon as a function of time. v(t) (b) What is the furthest distance the balloon could travel? Total distance = meters.
A small boat is being pushed up a ramp into the back of a flatbed truck. The boat is sitting at the top of the ramp, which is located 1.4 m above the ground. The boaters think the boat is safe there, and begin to walkaway. However, they have neglected the thin layer of ice that has formed on the ramp, which is angled at 30◦ up from the ground. Neglecting the friction between the boat and the ramp, how long do the boaters havebefore the boat reaches the bottom of the ramp?
A crate with a mass of 155 kg, starting from rest, slides down a ramp making an angle of 32 degrees with respect to horizontal. The ramp is 6 meters long. A constant frictional force of 200 N acts throughout the motion and a force Fis being applied by a rope as shown to prevent the block from sliding too fast. Suppose that while traveling at v=0.1 m/s down the ramp, at d=4meters from the end of the ramp, the rope breaks. Use the work- kinetic energy theorem to calculate the speed, in m/s, of the crate when it touches the bottom of the ramp. Use 9 = 9.8 m/s
A car weighing 2.5 metric tons and traveling at 90 km/h hits a 500 m long stretch of black ice. Unfortunately, due to skidding, neither accelerating nor braking has any effect on the speed! The driver manages to maintain steady straight direction of motion and the only impact is provided by the ice friction force, which is numerically equal to 4v² Newtons, where the velocity v of the car is measured in m/sec. (a) Using Newton's Second Law F = ma, set up a mathematical model for the position x(t) and velocity v(t) of the car as functions of time t. Start by drawing a diagram and choosing a consistent system of units based on kg, m, sec (1 ton = 1000 kg, 1 m/sec = 3.6 km/h, 1 N = 1 kg · m/sec²). Introduce and label the variables, show the units and write down the differential equations and the intial conditions. (b) Use the model in part a to calculate v(t) and x(t). Fully show the process of solving the initial value problems. (c) Based on your work so far, how long will it take to pass…
A ball rolls off the edge of a table. Let the time the ball leaves the table surface be t = 0. If the table is horizontal, its velocity as a function of time is given by ✓ = 1.10î - 9.80tĵ, with v in m/s and t in s. The ball's displacement from the edge of the table from t = 0 to t = 0.395 s (while it is in flight), is given by Ar = Jo Ar = 0.395 Use this theorem to perform the integration: v dt. [ [ P + Qf(x)] dx = p[ dx + Q f f(x) dx. P[ Consider the units and unit vectors to be the constants P and Q. Integrate to determine the ball's displacement (in m) from the table edge at 0.395 s. (Express your answer in vector form. Do not include units in your answer.) m
A projectile is thrown upward from the ground at 76.0° with the horizontal and returns to the ground 2.5 s later. Ignoring air friction (a) How fast was it thrown? (b) How far from its original position did it land? (c) How high above its original position did it go?
A 547g squirrel with a frontal surface area of 0.0145m2 falls to the ground from a 5.3m tree. Assume the density of air is 1.21kg/m3. Neglecting the drag force, what is the velocity, in meters per second, of a 56kg person after falling, from rest, by that same distance?
A plane has a mass of M = 201 tons takes-off at a speed of Vf = 243 km/hr. If it starts form rest, what should be the minimum acceleration to take off if the length of the runway is L = 1.7 km
Which of the following differential equations is the correct model if up is the positive direction? Consider an object of mass m that was thrown upwards and the magnitude of the force due to air resistance is 2v where v is the speed of the object in meters per second. pick (1) mv′=−mg−2v mv′=−mg+2v mv′=mg+2v mv′=mg−2v
*12-116. The automobile is originally at rest s = 0. If it then starts to increase its speed at v = (0.05t²) ft/s² , where t is in seconds, de- termine the magnitudes of its velocity and acceleration at s = 550ft.
A soldier jumps from a plane and opens his parachute when his velocity reaches the terminal velocity Vr. The parachute shows him down to his landing velocity of Vr. After the parachute is deployed, the air resistance force is proportional to the velocity squared, i.e., F = kV², where k is resistance coefficient. The soldier, his parachute, and his gear have a total mass of m. (a) Show that k = mg/V; (b) Develop a relation for the soldier's velocity after he opens the parachute at time 1 = 0. Parachute Figure Q5
A bicyclist can coast down a 6.17 degree hill at a constant speed of 6.64 km/h. If the force of air resistance is proportional to the speed vso that Fair = c v, calculate the average force (in N) that must be applied in order to descend the hill at 13.0 km/h. The mass of the cyclist plus bicycle is 77.8 kg.