Free fall

On the Moon, where there is no air, an astronaut dropped a hammer and a feather at the same time and both reached the ground at the same time. The scene is shown in the figure.

1. a) What does this fact show about falling objects when there is no air resistance?
2. b) What is the acceleration called with which objects fall on Earth, and what is its approximate value?

In free fall, the speed of an object increases by $9,8\ \text{m/s}$ every second. An object is dropped from rest.

1. a) Calculate its speed at $1\ \text{s}$, $2\ \text{s}$ and $3\ \text{s}$.
2. b) What acceleration does the object have during the fall, and which letter is used to represent it?

A stone is dropped from rest. With $g = 9,8\ \text{m/s}^2$, calculate its velocity after $2\ \text{s}$ of falling using $v = v_0 + g \cdot t$.

An object is dropped from rest. With $g = 9,8\ \text{m/s}^2$, calculate the distance it has fallen after $3\ \text{s}$ using $h = \frac{1}{2} g \cdot t^2$.

A coin falls from a height of $1,25\ \text{m}$. Take $g \approx 10\ \text{m/s}^2$.

1. a) How long does it take to reach the ground?
2. b) With what speed does it arrive?

A ball is thrown vertically upwards at $15\ \text{m/s}$. Take $g \approx 10\ \text{m/s}^2$.

1. a) How long does it take to reach its maximum height? Hint: at the highest point, the velocity is zero.
2. b) What maximum height does it reach above the release point?

A stone is thrown vertically upwards from a bridge at $10\ \text{m/s}$. Take $g \approx 10\ \text{m/s}^2$.

1. a) What maximum height does it reach above the level of the bridge?
2. b) How long does it take to pass the level of the bridge again?

You throw a ball vertically upwards at $20\ \text{m/s}$ from the ground, as shown in the figure. Take $g \approx 10\ \text{m/s}^2$.

1. a) What maximum height does it reach?
2. b) How much time passes until it returns to your hands?
3. c) With what velocity does it return? Compare it with the launch velocity and comment on the result.

A ball is thrown vertically upwards at $25\ \text{m/s}$ from the ground, as shown in the figure. Take $g \approx 10\ \text{m/s}^2$.

1. a) Calculate the maximum height and the time at which it reaches it.
2. b) Set up the equation to find at what times it passes through the height of $20\ \text{m}$ and solve it: you will get two solutions.
3. c) Calculate the velocity of the ball for each of these two solutions.
4. d) Explain the physical meaning of the two solutions and the relationship between the two velocities.

From the edge of a roof $40\ \text{m}$ above the ground, a ball is thrown vertically upwards at $10\ \text{m/s}$, as shown in the figure. Take $g \approx 10\ \text{m/s}^2$.

1. a) What maximum height does it reach above the roof? And above the ground?
2. b) How long does it take to go up?
3. c) Set up the position equation taking the ground as the origin and calculate the total time of flight until the ball reaches the ground.
4. d) With what velocity does it hit the ground?

From the top of a tower $80\ \text{m}$ high, a stone is dropped, and at the same instant, another stone is thrown vertically upwards from the ground at $40\ \text{m/s}$, as shown in the figure. Take $g \approx 10\ \text{m/s}^2$.

1. a) Write the height equations for each stone, $h_1$ and $h_2$, measured from the ground.
2. b) Calculate the instant at which they cross paths.
3. c) At what height do they cross paths?
4. d) Calculate the velocity of each stone at that instant and state whether each one is moving up or down.

A hot air balloon ascends at a constant velocity of $5\ \text{m/s}$. When it is $30\ \text{m}$ above the ground, a ballast bag comes loose. Take $g \approx 10\ \text{m/s}^2$.

1. a) Explain why the bag, upon coming loose, continues to move upwards for a moment instead of falling immediately.
2. b) Taking the ground as the origin and upwards as positive, set up the position equation of the bag and calculate the time it takes to reach the ground.
3. c) With what velocity does it hit the ground?