A skydive jumps out of a hovering helicopter.A few second later another skydiver jumps out and they both fall along the same vertical line.ignore air resistance so that both skydivers fall with the same acceleration.a)Does the difference in their speeds stay the same throughout the fall?b) Does the vertical distance between them stay the same throughout the fall?

In a local diner, a customer slides an empty coffee cup down the counter for a refill. The cup slides off the counter and strikes the floor at distance d from the base of the counter. (a) If the height of the counter is h, find an expression for the time t it takes the cup to fall to the floor in terms of the variables h and g. t =        (b) With what speed does the mug leave the counter? Answer in terms of the variables d, g, and h. v1 =        (c) In the same terms, what is the speed of the cup immediately before it hits the floor? v2 =        (d) In terms of h and d, what is the direction of the cup's velocity immediately before it hits the floor? ? =         radians

A car moves along a horizontal road with constant velocity VO,z i (44 m/s) i Vo = until it encounters a smooth inclined hill. It climbs the hill with constant velocity Ủ1 = V1,z î + V1‚y Ĵ = (38 m/s)i + (4.2 m/s) j as indicated in the figure. The period of time during which the car changes its velocity is At = 3.6 s. Y Part (a) Enter a symbolic expression for the average acceleration vector of the car during the given time period in terms of the variables in the problem and the standard unit vectors. Part (b) What is the magnitude, in meters per squared second, of the car's acceleration during the given time period.

Falcons are excellent fliers that can reach very high speeds by diving nearly straight down. To pull out of such a dive, a falcon extends its wings and flies through a circular arc that redirects its motion. The forces on the falcon that control its motion are its weight and an upward lift force—like an airplane—due to the air flowing over its wings. At the bottom of the arc, as shown, a falcon can easily achieve an acceleration of 15 m/s2. Suppose the falcon weighs 8.0 N and is turning with an acceleration of 15 m/s2 at the lowest point of the arc. What is the magnitude of the upward lift force at this instant?A. 8.0 N            B. 12 NC. 16 N             D. 20 N

A crate of mass m = 2.00 kg is released from rest at the top of an inclined plane as seen in the figure. The crate starts out at height = 0.100 m above the top of the table, the table height is H = 2.00 m, and 0 = 41.0⁰. H ↑ h i (a) What is the acceleration (in m/s2) of the crate while it slides down the incline? m/s² m (b) What is the speed (in m/s) of the crate when it leaves the incline? m/s (c) At what horizontal distance (in m) from the end of the table will the crate hit the ground? m O No (d) How long (in s) from when the crate is released does it hit the ground? S (e) Does the crate's mass affect any of your above answers? Yes

Two fan carts are on parallel inclined tracks are facing opposite directions. At t=0, the carts are 2.88 m apart with the fans on and they are both given a sharp push toward each other against the direction the fans are pushing them. Cart A begins (after the push) with a speed of 1.35 m/s to the right and has an acceleration of 0.44 m/s? to the left. Cart B begins (after the push) with a speed of 1.05 m/s to the left and has an acceleration to the right of 0.52 m/s?. (Hint: Keep your positive and negative directions consistent for both carts.) A a) At what two times do the two cars pass each other? b) What are the two positions at which the cars pass each other? c) What is the velocity of each car when they pass each other? d) Graph the motion of each on the position vs. time graphs and velocity vs. time graphs on the next page. time (s) time (s) (w) uojiisod velocity (m/ş)

5. A student throws a 0.1 kg ball into the air. (A) Just after the ball leaves their hand, it has a velocity of 5 m/s. (B) At the peak of its motion, it has a velocity of 2 m/s. Assuming no air resistance, to what height dịd the student throw the ball? Also, assume the ball started at h=0 (The zero-reference line is at the starting position of the ball). The energy chart is optional. KE- Vz- Poson A SystemFlow Poston KE- 1.2SJ@ A KE /2..1.2 KE- 0.25 @B Etr E, E Ea Et E, E En Energy Equation KETGPE = KE + GPE 6. A parachutist of mass 50.0 kg jumps out of a stationary balloon at a height of 1,000 meters. The system consists of the parachutist and the Earth, if the parachutist lands with a speed of 5.0 m/s, how much energy was transferred out of the system (so energy transferred to something else)? 7. Suppose the spring below has a spring constant of 50. N/m. The box has a mass of 8.0 kg and rests on a surface of negligible friction. In the diagram above, the spring was compressed 4.0 m.…

You throw a ball on planet X where g is not the same as on Earth. The figure below shows the vertical velocity of the ball after it leaves your hand. Air resistance is not important. v(m/s) 18.0 12.0 6.0 -6.0 -12.0 -18.0 1.0 2.0 3.0 t(s)

A rocket is launched at an angle of 60.0° above the horizontal with an initial speed of 95 m/s. It moves for 3.00 s along its initial line of motion with an acceleration of 32.0 m/s2. At this time its engines fail and the rocket proceeds to move as a free body. a. Find the maximum altitude reached by the rocket. _______m b. Find its total time of flight. _______ s c. Find its horizontal range _______ m

An airplane is moving sideways at a constant pace, and drops two packages. Package #1 is light, while package #2 is heavy. For this problem, ignore air resistance. Package(s)  will reach the ground first? Package 1 will land in front of below or behind or beside the plane, and package 2 will land in front of below or behind or beside the plane. Package 1 will land in front of below or behind or beside the other package?