A child plays on an escalator by going up and down while the escalator is moving. When he runs upward in the same direction with the escalator he can reach the upper level in 27 seconds. Then he runs downward in the opposite direction of the escalator, and he reaches the lower level in 79 seconds. The child has the same average speed relative to the escalator in both cases. If the speed of the escalator is 1.58 m/s, calculate the speed of the child.

While moving from her third-storey apartment, a university student decides to lower her couch through her window using ropes. During the process, the ropes snap and the couch, which is 12.0 m above the ground, falls to the ground below. Her friends, who are both 1.50 m tall, notice the accident when the couch is directly above them. Determine the time they have to get out of the way.

A student launches a small rocket which starts from rest at ground level. At a height h=1.04km, the rocket reaches a speed of vf=391m/s. At that height, the rocket runs out of fuel, so there is no longer any thrust propelling it. After the rocket's engine turns off at a height of h=1.04km, it continues to move upward due to the velocity that it reached. What is the rocket's acceleration, in meters per squared second, during the period from engine shutoff until it returns to the ground? Ignore air resistance.

An object is thrown vertically upwards with an initial velocity of +5 m/s and then comes back down. What is the final velocity when it returns to its initial height? Ignore air resistance.

A stone is thown from the top edge of a cliff with an initial speed of V0 = 15 m/s . The stone takes 3 seconds to each the bottom. What is the height of the cliff. (air resistance is negligible).

An attacker at the base of a castle wall 3.65 m high throws a rock straight up with speed 7.40 m/s from a height of 1.55 m above the ground. (a) Will the rock reach the top of the wall? (b) If so, what is its speed at the top? If not, what initial speed must it have to reach the top? (c) Find the change inspeed of a rock thrown straight down from the top of the wall at an initial speed of 7.40 m/s and moving between the same two points. (d) Does the change in speed of the downward-moving rock agree with the magnitude of the speed change of the rock moving upward between the same elevations? (e) Explain physically why it does or does not agree.

In 1948 United States Air Force pilot Gail halvorsen became known as the Berlin Candy Bomber when he began dropping candy bars and Bubblegum to the children of Berlin. If he was flying with a forward velocity of 100 meters per second at a low altitude of 1000 m how far from the Berlin Wall would he have to release the candy so that it would land in the city?

Henrietta is jogging on the sidewalk at 3.05 m>s on the way to her physics class. Bruce realizes that she forgot her bag of bagels, so he runs to the window, which is 38.0 m above the street level and directly above the sidewalk, to throw the bag to her. He throws it horizontally 9.00 s after she has passed below the window, and she catches it on the run. Ignore air resistance. (a) With what initial speed must Bruce throw the bagels so that Henrietta can catch the bag just before it hits the ground? (b) Where is Henrietta when she catches the bagels?

A long jumper leaves the ground at an angle of 29 degrees and lands 8.2 meters away. With what speed did he jump? Please answer in m/s

A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof a time of 1.12 s later. You may ignore air resistance. If the height of the building is 20.4 m, what must the initial speed be of the first ball if both are to hit the ground at the same time? Consider the same situation, but now let the initial speed v0 of the first ball be given and treat the height h of the building as an unknown. What must the height of the building be for both balls to reach the ground at the same time for v0 = 8.50 m/s. If v0 is greater than some value vmax, a value of h does not exist that allows both balls to hit the ground at the same time. Solve for vmax. If v0 is less than some value vmin, a value of h does not exist that allows both balls to hit the ground at the same time. Solve for vmin.