An 88 kg fireman slides 5.9 meters down a fire pole. He holds the pole, which exerts a 520 N steady resistive force on the fireman. At the bottom, he slows down to a stop in 0.43 m by bending his knees. Determine the acceleration while stopping and the ti

To find the acceleration of the fireman while stopping, we first need to find the net force acting on him. We can use the equation: Net force = Force applied - Force resisting motion In this case, the force applied is the force of gravity, which is equal to the fireman's weight: Force applied = 88 kg * 9.8 m/s^2 = 862.4 N The force resisting motion is the force exerted by the pole, which is 520 N. Net force = 862.4 N - 520 N = 342.4 N Now we can use Newton's second law of motion, which states that the net force acting on an object is equal to the object's mass times its acceleration: Net force = mass * acceleration We can rearrange this equation to solve for the acceleration: Acceleration = Net force / mass Acceleration = 342.4 N / 88 kg = 3.89 m/s^2 Therefore, the acceleration of the fireman while stopping is 3.89 m/s^2. To find the time it takes for the fireman to stop after reaching the ground, we can use the equation: Final velocity^2 = Initial velocity^2 + 2 * acceleration * distance The initial velocity is the velocity at the bottom of the pole, which is equal to the velocity of the fireman sliding down the pole. We can use the equation for gravitational potential energy to find this velocity: Initial potential energy = Final kinetic energy mgh = 1/2 * mv^2 where m is the mass of the fireman, g is the acceleration due to gravity (9.8 m/s^2), h is the height of the pole (which we assume to be negligible), and v is the velocity we want to find. Solving for v, we get: v = sqrt(2 * mgh / m) v = sqrt(2 * 88 kg * 9.8 m/s^2 * 5.9 m / 88 kg) v = 7.84 m/s Now we can use the equation above: 0^2 = 7.84 m/s^2 + 2 * (-3.89 m/s^2) * 0.43 m Solving for the final velocity, we get: Final velocity = sqrt(7.84 m/s^2) Final velocity = 2.80 m/s The time it takes for the fireman to stop is the time it takes for him to decelerate from a velocity of 2.80 m/s to a velocity of 0 m/s. We can use the equation: Final velocity = Initial velocity + acceleration * time 0 m/s = 2.80 m/s + (-3.89 m/s^2) * time Solving for time, we get: time = 2.80 / 3.89 s time = 0.72 s Therefore, it takes the fireman 0.72 s to stop after reaching the ground.