A gun is fired straight up. Assuming that the air drag on the bullet varies quadratically with speed, show that the speed varies with height according to the equations o = Ae k - (upward moton) -2kr k =-Be (downward moton) in which A and B are constants of integration, g is the acceleration of gravity, and k =cz/m where cz is the drag constant and m is the mass of the bullet. (Note: x is measured positive upward, and the gravitational force is assumed to be constant.)
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- Consider an object on an incline where friction is present. The angle between the incline and the horizontal is θ and the coefficient of kinetic friction is μk. a.) Find an algebraic expression for the acceleration of this object. Treat down the incline as the positive direction. b.) Calculate the acceleration, in meters per second squared, of this object if θ = 31° and μk = 0.34. Treat down the incline as the positive direction.A ball with mass 0.1 kg is thrown upward with initial velocity 5 m/s from the roof of a building 60 m high. Assume there is a force due to |v| air resistance of magnitude directed opposite to the velocity, where 30 the velocity v is measured in m/s. NOTE: Use g=9.8 m/s² as the acceleration due to gravity. Round your answers to 2 decimal places. a) Find the maximum height above the ground that the ball reaches. Height: m b) Find the time that the ball hits the ground. Time: seconds c) Use a graphing utility to plot the graphs of velocity and position versus time.For Problems 1 and 2, use the following formula to describe the magnitude of a drag force: 1 D = — -CA pv² 2 FD Problem 1: When a car is traveling at a speed of 30 km/h, it experiences a drag force of magnitude F. If the car increases its speed to 40 km/h, what then will be the drag force it experiences? Assume the drag force is proportional to the square of speed.
- You are pulling a 72-kg box at a constant speed of 7.4 m/s. If you're pulling the rope with a force of 300 N at an angle of 37° measured above the horizontal, what is the coefficient of friction between the box and the ground?A skater of mass m standing on ice throws a stone of mass M with speed v in a horizontal direction. Find the distance over which the skater will move in the opposite direction if the coefficient of kinetic friction between the skater and the ice is ?k . (Use any variable or symbol stated above along with the following as necessary: g.)Δx =At Ted's request, Bill pushes the pizza box across the granite countertop towards Ted. When the box leaves Bill's hand it is sliding at 2.60 m/s. The box comes to rest over a distance of 110 cm. What is the coefficient of kinetic friction, uk, between the pizza box and the countertop? (Ignore air drag.)