We can use a kinematics equation to solve this problem:

Rearranging for change in distance:

We have all of the values we need, so we can solve the problem:

Note that the acceleration is negative since she is decelerating from a positive velocity.

We can use the follow kinematics equation to solve this problem:

Rearranging for change in x, we get:

Now plugging in values for each variable:

To solve this problem we will go in the following steps:

1. Calculate linear velocity parallel with slope

2. Calculate vertical component of velocity

3. Calculate time it takes to drop 12m

So first, we will use the cosine function:

Rearranging:

Plugging in our value:

Now to calculate the vertical component, we will use the sine function:

Rearranging

Now using this to calculate the time it takes to drop :

Since the arrow is shot straight up in the air, we can calculate how long it takes for the arrow to reach its high point (where it will have a velocity of 0):

Furthermore, this will be the same amount of time it takes to get to its original position. Then we just need to calculate how long it takes the arrow to travel from its original position to the ground, using the follow kinematics equation:

Plugging in our values:

Rearranging:

Using the quadratic equation, we get:

 or 

Since we can't have a negative time, the first option is the correct one. Adding this to our other time, we get:

Alternatively, we could have solved the equation by putting the initial conditions in the kinematic equation.

However, the first method emphasizes the importance of being able to solve a problem multiple different ways and incorporates multiple concepts surrounding projectile motion.

We can solve these problems using kinematic equations.  First we start with:

We know that the final velocity is  because at the top of an arc the water heater doesn't have vertical movement.  The acceleration is due to gravity, and the time is only half the time that was given in the problem (half the time is the water heater going up, the other half is it falling back to the ground).

When we know the initial velocity of the water heater we can then use:

First we must find the original object's mass using the equation . . We then double the mass for the second object and again use  . Solve for acceleration using  and .

The acceleration of an object due to gravity is . If you multiply this value by one second, you can see that an object increases by a speed of  per second. After one second the ball is traveling  faster.

The equation for acceleration is . The final velocity minus the initial velocity is  and the change in time is . When dividing the change in velocity by the change in time you receive the answer  which means that the car is decelerating due to the negative sign.

To find the acceleration, use the kinematic equation 

*the rider's acceleration will match that of the motorcycle.