A spacecraft is moving in gravity-free space along a straight path when its pilot decides to accelerate forward. He turns on the thrusters, and burned fuel is ejected at a constant rate of 2.0 × 10² kg/s, at a speed (relative to the rocket) of 2.5 × 10² m/s . The initial mass of the spacecraft and its unburned fuel is 2.0 × 104 kg, and the thrusters are on for 30 s. a. What is the thrust (the force applied to the rocket by the ejected fuel) on the spacecraft? b. What is the spacecraft's acceleration as a function of time? 20 25-3

During terrible weather at a ski-flying world championship, a ski jumper tried to adjust for bad conditions midway down the ramp but completely lost control and tumbled wildly off the side at its bottom into a scattering crowd. The 73-kg jumper left the ramp about 45 m lower than his starting position. If the ski jumper had simply fallen straight down 45-m rather than skiing down a ramp, would his kinetic energy increase?

During an Olympic 100-m sprint race, Usain Bolt, the world record holder in that race, quickly accelerates to his top speed of 12.4 m/s. Analysis of his technique has shown that each of his feet make contact with the ground for 0.0800 s, exerting a force of magnitude 2.80 x 10° N during this contact. This allows the 94.0 kg Bolt to leap forward and remain airborne for 0.120 s until the next foot touches the ground. (Ignore air resistance.) (a) What are the magnitudes of the horizontal and vertical components of the force (in N) Bolt's feet exert on the ground? (Round your answers to at least three significant figures.) horizontal N vertical (b) Assuming that the sprinter accelerates at a constant rate while his feet are in contact with the ground and does not slow down when he is airborne, by what amount does Bolt's horizontal speed (in m/s) increase with each step? (Round your answer to at least three significant figures.) m/s (c) Assuming that the sprinter's speed increases at a…

During the entry of the space shuttle into the earth’s atmosphere, maximum stagnation point heating occurs at the trajectory point corresponding to an altitude of 68.9 km, where ρ∞ = 1.075 × 10−4 kg/m3, and a flight velocity of 6.61 km/s. At this point on its entry trajectory, the shuttle is at a 40.2 degree angle of attack, which presents an effective nose radius at the stagnation point of 1.29 m. If the wall temperature is Tw = 1110 K, calculatethe stagnation point heating rate.

Small steel balls, each with a mass of 150 g, enter the semicircular trough (Radius =0.92 m) in the vertical plane with a horizontal velocity of VA=7.9 m/s at A. Friction is negligible. UB B VA A velocity at C (m/s) a. 6.66 о Б.7.99 c. 5.33 d. 9.33 e. 2.66 normal reaction at C velocity at B (m/s) О а. 6.16 b. 5.13 C. 4.11 d. 3.08 е. 2.05 O O

A block with mass 0.400 kg is on a horizontal frictionless surface and is attached to a horizontal compressed spring that has force constant k=200N/m The other end of the spring is attached to a wall. The block is released, and it moves back and forth on the end of the spring. During this motion the block has speed 3.00 m/s when the spring is stretched 0.160 m. During the block's motion, what is the maximum distance the spring is compressed from its equilibrium position? When the spring has its maximum compression, what is the speed of the block and what is the magnitude of the acceleration of the block?