An astronaut in her space suit has a total mass of 87.0 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while she’s on a spacewalk. Initially at rest with respect to her spacecraft, she throws her 12.0-kg oxygen tank away from her spacecraft with a speed of 8.00 m/s to propel herself back toward it (Fig. P6.25). (a) Determine the maximum distance she can be from the craft and still return within 2.00 min (the amount of time the air in her helmet remains breathable). (b) Explain in terms of Newton’s laws of motion why this strategy works.

A 4.0 kg ball is traveling at 11.9 m/s and strikes a wall. The ball bounces off the wall with a velocity of 4.2 m/s in the opposite direction. If the ball is in contact with the wall for 0.10 seconds, then the magnitude of the average force on the ball during contact is? Enter only a numerical answer. Do not include units in the answer box, else your response will be counted as incorrect.

A 66.0-kg athlete leaps straight up into the air from a trampoline with an initial speed of 7.5 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? This answer has not been graded yet. (b) Select the height at which the athlete's speed is 7.5 m/s as  y = 0.  What is her kinetic energy at this point? JWhat is the gravitational potential energy associated with the athlete? J(c) What is her kinetic energy at maximum height? JWhat is the gravitational potential energy associated with the athlete? J(d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. m(e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer. m/s

At the center of a 47.0 m diameter circular ice rink, a 56.0 kg skater traveling north at 2.60 m/s collides with and holds onto a 59.0 kg skater who had been heading west at 1.05 m/s. How long (in seconds) will it take them to reach the edge of the rink assuming negligible friction and drag?

A gun fires a 21-gram bullet on a 1.8 kg wooden block hanging vertically at the end of string (The other end of the string is attached to a ceiling). The bullet embeds in the block, which swings upward a height of H. The speed of the bullet when leaving the gun is 250 m/s. Find H.