Understand the Acceleration Due to Gravity Formula and More!

At a waterpark, sleds with riders are sent along a slippery, horizontal surface by the release of a large, compresesed spring. The spring with a force constant k= 4000N/m and negligible mass rests on the frictionless horizontal surface. One end is incontact witha stationary wall. A sled and rider with total mass 70.0kg are pushed against the other end, compressing the spring 0.375m. The sled is then released with zero initial velocity. What is the sled's speed when the spring a) returns to its uncompressed length? b) is still compressed 0.200m?

A race driver has made a pit stop to refuel. Afterrefueling, he leaves the pit area with an acceleration whosemagnitude is ${\displaystyle 6.0\frac{m}{s^2}}$ ; after 4.0s he enters the mainspeedway. At the same instant, another car on thespeedway and traveling at a constant speed of 70.0m/sovertakes and passes the entering car. If the entering carmaintains it acceleration, how much time is required for it tocatch the other car? 
I tried to find the V for the car in the pit area. Isthat the right first step; what do I do next? Any help would begreat.

Two astronauts, one mass 60 Kg and the other 80 Kg, areinitially at rest in outer space. They then push each otherapart. How far apart are they when the lighter astronaut hasmoved 12 m. Is it -12m? velocities should be the samein free fall.

A 500 g ball swings in a vertical circle at the end of a1.5-m-long string. When the ball is at the bottom of the circle,the tension in the string is 15 N. 
What is the speed of the ball at that point?

The tires of a car make 65 revolutions as the car reduces its speed uniformly from 100 km/h to 50 km/h. The tires have diameter of 0.80 m. a) What was the angular acceleration? b)If the car continues to decelerate at this rate, how much more timeis required for it to stop?
For part a, I thought my method was pretty legitimate, but myanswer didn't match the one in the back of the book. The backof the book had the answer -4.4 ${\displaystyle ra\frac{d}{s^2}}$, whereas Igot $-1.59\cdot {10}^4$ ${\displaystyle ra\frac{d}{s^2}}$

A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 220 mph at an altitude of 800 m. The positive x and y directions are defined. For all parts, assume that the "island" refers to the point at a distance D from the point at which the package is released, as shownin the figure. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is g=9.80 .

A swimmer is capable of swimming 0.45m/s in still water (a) If sheaim her body directly across a 75 m wide river whose current is0.40m/s how far downstream ( from a point opposite her startingpoint ) will she land ? (b) how long will it take her to reach theother side

A car is initially going 50 ft/sec brakes at a constant rate (constant negative acceleration), coming to a stop in 5 seconds.
a) graph the velocity from $t=0$ to $t=5$
b) how far does the car travel?
c) how far does the car travel if its initial velocity isdoubled, but it brakes at the same constant rate?

A loud speaker of mass 19.0 kg is suspended a distance of 1.00 m below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of 3.30 m.
A) What is the tension in each ofthe cables? (Use ${\displaystyle 9.80\frac{m}{s^2}}$ for the magnitude of the acceleration due to gravity.)

Two blocks with masses 4.00 kg and 8.00 kg are connected by string and slide down a 30.0 degree inclined plane. The coefficient of kinetic friction between the 4.00-kg block and the plane is 0.25; that between the 8.00-kg block and the plane is 0.35.
a) Calculate the acceleration of each block
b) Calculate the tension in the string
c) What happens if the positions of the block are reversed, so that the 4.00-kg block is above the 8.00-kg block?

An atomic nucleus initially moving at 420 m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350 m/s. If the alha particle has a mass of 4.0u and the original nucleus has a mass of 222u. What speed does the alpha particle have when it is emitted?

A student drops two metallic objects into a 120 g steel container holding 150 g of water at 25°C. One object is a240 g cube of copper that is initially at 85°C, and the other is a chunk of aluminum that is initially at 5.0°C. To the surprise of the student, the water reaches a final temperature of 25°C, exactly where it started. What is the mass of the aluminum chunk?

A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 65.0 m/s at an angle of 37 degrees with the horizontal. (a) determine the time taken by the projectile to hitthe point P at ground level. (b) determine the range X of the projectile as measured from the base of the cliff at the instant just before the projectile hits point P. Find (x) the horizontal and vertical components of its velocity and (d) the magnitude of the velocity and (e) the angle made by the velocity vector with the horizontal (f) Find the maximum height above the cliff top reached by the projectile.

A diving borad 3.00 m long is supported at a point 1.00 m fromthe end, and a diver weighing 500 N stands at the free end. The diving board is of uniform cross section and weighs 280N. 
A. Find the force at the support point. 
B. Find the force at the end that is beng held down.

An exceptional standing jump would raise a person 0.80 m off the ground. To do this, what force must a 66-kg person exert against the ground? Assume the person crouches a distance of 0.20 m prior to jumping, and thus the upward force has this distance to act over before he leaves the ground.

In a scene in an action movie, a stuntman jumps from the top of one building to the top of another building 4.0m away. After a running start, he leaps at a velocity of 5.0 m/s at an angle of 15degrees with respect to the flat roof. Will he make it to the other roof, which is 2.5m shorter than the building he jumps from?

A 0.145 kg baseball pitched at 39.0 m/s is hit on a horizontal line drive straight back toward the pitcher at 52.0 m/s. If the contact time between bat and ball is ${\displaystyle 1.00\times {10}^{-3}}$ s,calculate the average force between the bat and ball during contest.

A 7.0- g bullet is fired into a 1.5- kg ballistic pendulum.The bullet emerges from the block with a speed of 200 m/s, and theblock rises to a maximum height of 12 cm. Find the initial speed ofthe bullet.

Torricelli's Law provides the volume V of water still in the tank after t minutes if a tank holds 5000 gallons of water and the water drains from the bottom of the tank in 40 minutes.${\displaystyle (1-{\frac{t}{40}}^2)5000=V0\le t\le 40}$.
Find the rate at which the tank's water is emptying after (a) five minutes and (b) ten minutes. At what time is the water flowing out the fastest? The slowest?

In an inkjet printer, letters are built up by squirting drops of ink horizontally at a sheet of paper from a rapidly moving nozzle. The Pattern on the paper is controlled by an electrostatic valve that determines at each nozzle position whether ink is squirted onto thepaper or not. The ink drops have a radius 15.0${\displaystyle \mu m}$ and leave the nozzle and travel horizontally toward the paper at speed v=18.0 m/s . The drops pass through a charging unit that gives each drop a positive charge by causing it to lose some electrons. The drops then pass between parallel deflecting plates of length ${\displaystyle D_0=2.45}$ cm , where there is a uniform vertical electric field with magnitude ${\displaystyle E=8.40\times {10}^4}$ N/C
If a drop is to be deflected a distance d= 0.270 mm by the time it reaches the end of the deflection plate,what magnitude of charge q must be given to the drop? (Assume that the density of the ink drops 1000 ${\displaystyle k\frac{g}{m^3}}$, and ignore the effects of gravity.)