Hey I need help in these questions An object of mass 250 kg

Hey,

I need help in these questions.

An object of mass 250 kg is released from rest 1500000 m above the ground and allowed to fall under the influence of gravity. Assume the gravitational force is constant, with g=9.81m/sec² , and the force due to air resistance is proportional to the velocity of the object. Find the proportionality constant k (in kg/sec) if the terminal speed of the object is 490.5 m/sec.

An object of mass 10 kg is released from rest 58860 m above the ground and allowed to fall under the influence of gravity. Assume the gravitational force is constant, with g=9.8 m/sec² , and the force due to air resistance is proportional to the velocity of the object with proportionality constant k= 5 kg/sec. Approximate when (in seconds) the object will strike the ground.

Thank you

Solution

Ans-

To the right is the \"free-body diagram\" showing the pertinent forces if the back wheel has not left the ground. The weightmg acts at the center of gravity of the bike+rider and each wheel has a normal force (N) and frictional force (f) from the ground. The bike has an acceleration a in the direction of the frictional forces, so f₁+f₂=ma. The system is in equilibrium in the vertical direction, so N₁+N₂-mg=0. The bike is also in rotational equilibrium so all the torques about any axis must be zero; summing torques about the front axle,Rf₁+Rf₂+DN₂-dmg=0 where R is the radius of the wheel, D is the distance between axles, and dis the horizontal distance between the front axle and the center of gravity. Now, suppose that the rear wheel is just about to leave the ground; then N₂=f₂=0. The three equations then become N₁-mg=0, f₁=ma, and Rf₁-dmg=0. Putting the second equation into the third and solving for the acceleration, a=g(d/R); if you are slowing down any faster than this, your rear wheel will lift off the ground and the bike will no longer be in rotational equilibrium. If a is really big, you will keep rotating until your center of gravity is forward of the front axle; then you will not be able to stop the bike from rotating all the way over and crashing you on the ground. This actually happened to me once when I was mountain biking with my son and I broke a couple of ribs! I do not understand your second question.