Consider the problem of dropping an object from a high bridge. We'll consider two problems 40...
1. A rocket is launched vertically from the Earth, and the thrust (pushing force) from the engines is directed upward, and has a magnitude of 5.00 x 106 N. The mass of the rocket is initially 2.00 x 105 kg. (a) What is the initial acceleration of the rocket, assuming you can neglect air resistance? (b) After the rocket has been in flight for a while, burning and exhausting a lot of fuel, its mass has decreased to 1.20 x 105 kg, and...
When an object falls in Earth's gravitational field (think of a skydiver jumping from an airplane or a marble falling in a tank of oil), it accelerates due to the force of gravity. If gravity were the only force acting on the object, then all objects-elephants and feathers alike would fall at the same rate. But gravity is not the only force present. Moving objects also experience resistance or friction from the surrounding medium; it would be air resistance for...
2. Suppose an object of mass 15 kg is dropped from a height near the surface of the Earth, so the acceleration due to gravity is -9.8, and assume the drag due to air 0.47. Assume the object's position is measured in meters above the ground, so velocity (a) Write down, but do not solve, a differential equation whose solution would give resistance is proportional to the square of object's velocity, with drag coefficient γ and acceleration are both negative...
3) The velocity v(t) of a skydiver falling to the ground is governed by the equation m dv/dt mg-kv, where g is the acceleration due to gravity, and k>0 is the drag constant associated with air resistance a) Find the analytical solution for V(t), assuming v(0) 0 b) Find the limit of v(t) as t goes to infinity. This is known as the terminal velocity. c) Give a graphical analysis of this problem, and re-derive the formula for the terminal...
2. An object of 5 kg is released from rest 1000 meters above the ground level and allowed to fall under the influence of gravity. Assuming that the force due to air resistance is proportional to the velocity of the object with proportionality constant k = 50 kg/sec determine the formula for the velocity of the object 3. A rocket having an initial mass mo kg is launched vertically from the surface of the Earth. The rocket expels gas at...
Suppose an object falls from a great height on a planet where the acceleration constant of gravity is g = 7.29. Suppose that the resistance of the atmosphere is proportional to the square of the speed of the object with constant of proportionality k = 0.36. Establish and solve an Initial Value Problem to express the velocity of the object as a function of time. Find the terminal velocity of the object. Graph this function. Then express the fallen distance...
Solve & Explain Steps Please. 6. Consider the problem of a free falling object with mass M. Assume that only gravity and air resistance act upon the object. (a) As a first model, let us suppose that the air resistance is proportional to the velocity v(t) of the object. Newton's second law of motion gives the DE M)go),20 More exactly, this is a first order linear DE with constant coefficients: Mw,(t) + ku(t) = Mg , t 2). Suppose that...
please explain the answer 1) Up until now we have always ignored air resistance. We should now add it. Let us just think of simple 1-dimensional problem, dropping a ball of mass m from a height H but 2 with air resistance. We can model the air resistance as a force proportional to the velocity, fair = bv. The coefficient bis a constant. (For this problem you can use calculus textbooks or wolfram alpha to do the calculus.) What are...
1) Up until now we have always ignored air resistance. We should now add it. Let us just think of simple 1-dimensional problem, dropping a ball of mass m from a height H but with air resistance. We can model the air resistance as a force proportional to the velocity, fair = bu. The coefficient b is a constant. (For this problem you can use calculus textbooks or wolfram alpha to do the calculus.) • What are the units on...
please explain the answer. 1) Up until now we have always ignored air resistance. We should now add it. Let us just think of simple 1-dimensional problem, dropping a ball of mass m from a height H but 2 with air resistance. We can model the air resistance as a force proportional to the velocity, fair = bv. The coefficient bis a constant. (For this problem you can use calculus textbooks or wolfram alpha to do the calculus.) What are...