A student throws a set of keys vertically upward to his fraternity brother, who is in a window 3.95 m above. The brother's outstretched hand catches the keys 1.40 s later. (Take upward as the positive direction. Indicate the direction with the sign of your answer.) (a) With what initial velocity were the keys thrown? (m/s) (b) What was the velocity of the keys just before they were caught? (m/s)

In a local bar, a customer slides an empty beer mug down the slippery counter for a refill. The bartender is momentarily distracted and does not see the mug, which slides off of the counter and strikes the floor 2.11 m from the base of the counter. If the height of the counter is 1.62 m high, what is the magnitude of the velocity of the mug as it left the counter? Your Answer: Answer

A long-jumper sets a personal best of 5.92 m in a jump for which the launch angle was 29.4 degrees above horizontal. What was the launch speed, in m/s?

Near the end of a marathon race, the first two runners are separated by a distance of 45.0 m. The front runner has a velocity of 3.50 m/s, and the second a velocity of 4.25 m/s. (a) What is the velocity of the second runner relative to the first? (Enter a number. Enter your answer in m/s faster than the front runner.) X m/s faster than the front runner (b) If the front runner is 250 m from the finish line, who will win the race, assuming they run at constant velocity? The first runner will win. The second runner will win. (c) What distance (in m) ahead will the winner be when she crosses the finish line? (Enter a number.) X m