Use the kinematic equation .

Negative acceleration because the projectile was slowing down.

To find its speed before leaving the ramp,.

Yes, it will be moving faster than necessary. 

Use the kinematic equation .

Since the object was dropped and starts at position 0 in the hand, the first two terms initial position and initial velocity become 0.

Since the object is just falling it is only subject to the acceleration of gravity (especially since we are ignoring frictional forces).

So the final speed is equal to the time multiplied by the acceleration of gravity: 

The apple is flying straight up with an initial velocity of , with the only force acting on it being gravity. Gravity will provide the apple with an acceleration of  directed downwards. The following kinematic equation is needed to solve for the time it takes for the apple to hit the ground:

The first step is to see how long it takes the apple to get to the highest point of its journey. At that point, the velocity will have slowed to zero:

Solving for t gives us:

Since it took the apple 2.04 seconds to get to the top, that means it will take the apple another 2.04 seconds to get back to its starting point. This also means that the velocity of the apple when it reaches is starting point will be equal and opposite its starting velocity:

To find the amount of time it takes the apple to reach the ground, the following kinematic equations are used:

And:

Therefore, the total time it takes for the apple to reach the ground is:

We can split this question up into the x-direction and y-direction. In the y-direction, the object's acceleration is zero since it's going to remain in contact with the ground. We now can write our  equation (let the up direction be positive). Since it's not accelerating, we have

. 

 denotes the normal force. We know that the mass is  and that , so we can solve for the normal force, which we'll later use to find the force of friction. 

The force of friction  is equal to  (where  denotes the coefficient of friction), so

In the x-direction, we'll denote right as positive. The forces in the x-direction are  right,  left, and . Now we can write our  equation as 

Using this acceleration, we can use kinematics to solve for the distance the object will travel in  seconds. We have time and acceleration, but we need distance, so we'll use the equation: 

Momentum is always conserved in physical collisions. Momentum is represented by the equation:

When the cars collide the momentum of each car contributes to a total momentum of a new object that is a combined mass of the original two cars. The equation for this would appear as follows where car 1 is object one, car 2 is 2, and the object after the collision is object 3:

Because the mass of the first car is 1250 kg and the mass of the 2nd car is 1400kg, their combined mass for the resulting object is 2650 kg. By plugging in values, the velocity of this combined object is found to be:

Due to conservation of momentum, all of the momentum that the ball has must be conserved after the collision. Because the cue ball completely stops moving after the collision it has no momentum meaning that all of the momentum is transferred to the 8 ball. Momentum is represented by this equation:

Since the momentum must be equal before and after the collision, this equation can be formulated for this problem:

Where the cue ball is object 1 and the 8 ball is object 2. By plugging in the given values it is possible to find the velocity of the 8 ball after the collision. 

Solving for  gives a velocity for the 8 ball of 

In order to start this problem, a free body diagram illustrating all the forces acting on the object must be drawn. Because there are only 2 forces acting on the object the free body diagram would appear as follows (not to scale):

T1 stands for the tension in the rope created by body builder 1, T2 stands for the tension created by body builder 2. The total net force acting on the object, in the direction of body builder 1 is equal to

Newton's second law relates force, mass, and acceleration with the following equation:

By plugging in the given values for force and mass, acceleration is found to be:

The force-momentum relationship is:

Since both force and change in time are located on the left side of the equation, they are inversely proportional. Therefore, if the force doubles, the inverse must be true about the time. This would halve the time necessary for the cars to bump.