**1. 2.56 s**

First of all, we need to calculate the time it takes for the bag to fall down and reach the bottom of the well; this can be done by using the equation

where

is the acceleration of gravity

t is the time

We now that the distance covered is d = 30 m, so we can solve for t:

Now we also have to calculate the time it takes for the sound to cover the 30 m and reach the robber, which is:

So, the robber will hear the splash after a total time of

**2. 122.5 m**

For this problem, we can use again the following equation:

where

is the acceleration of gravity

t is the time

Here we know that the total time of the fall of the penny is

t = 5 s

So, the distance covered by the penny (which is equal to the heigth of the building) is

**3. -14 m/s**

For this problem, we can use the following equation:

where

v is the final velocity

u = 0 is the initial velocity

is the acceleration of gravity

d = 10 m is the distance covered (the height of the tower)

Solving for v,

And since the velocity points downward, we can write it as -14 m/s.

**4. 3.76 m/s**

We can solve this problem by using the equation

where:

v is the speed of the player at its point of maximum height

u is his speed as he leaves the floor

is the acceleration of gravity (we take it negative as we consider upward as positive direction)

d = 0.72 m is the maximum height reached above the floor

At the point of maximum height, the velocity is zero: v = 0. Therefore, we can solve the formula for u, the initial speed:

**5. 21.3 m, -20.6 m/s**

a) Taking downward as positive direction, we can use the equation

where

u = 3 m/s is the initial velocity

t = 1.8 s is the time

is the acceleration of gravity

Substituting, we find d, the depth of the hole:

b)

The velocity of the stone at time t is given by

Substituting,

And if we consider upward as positive direction, this becomes -20.6 m/s.

**6. 17.2 m/s, 15.1 m, see attachment for the graphs**

a. The time taken for the ball to reach the maximum heigth is half the total time:

We can now use the equation

where

v = 0 is the velocity at the maximum height

u is the initial velocity

t = 1.75 s is the time

is the acceleration of gravity

Solving for u,

b.

We can calculate the maximum height using

Solving for d,

c. See attachments

The displacement increases as the ball goes higher until it reaches its maximum height (15.1 m), then it decreases until the ball reaches again the position d=0.

The velocity is obtained by computing the slope of the displacement-time graph. Its initial value is 17.2 m/s, then it decreases constantly until it reaches zero (point of maximum height), then it becomes negative and continues decreasing (increasing in magnitude, as the ball accelerates downward)

The acceleration is obtained from the slope of the velocity-time graph. Since the motion of the ball is free fall, the acceleration is constant and equal to -9.8 m/s^2.

**7. 57.2 m**

The time it takes the balloon to fall to the ground is given by:

where

d = 40 m is the heigth

is the acceleration of gravity

Solving for t,

The distance covered by the truck during this time is

where v = 20 m/s is the speed of the truck. Substituting,

Therefore, the truck must be 57.2 m far when the vandal drops the balloon.