The report should have the following five sections. Each section must be written by a separate student. The whole report must be in a single Google Colab file and attached from Google Drive into the associated Google Classroom assignment.

A projectile

For this experiment you have to use the following apparatus: a table, a bench, a ramp, some marble balls, 3 white recording papers, 3 carbon papers, some adhesive tape for fixing the papers on the table or bench, a long meter scale to measure long heights and lengths, a short meter scale for measuring short distances on the recording papers, and a weight scale to measure the mass of a ball.

The setup is briefly sketched through the following points (elaborate in the report).

1. A bench is placed on a table. There must be enough space in front of the bench for the balls to bounce.
2. A ramp is placed on the bench.

Using the six measurements you will have to calculate the following quantities.

Time for the ball to leave the ramp and reach point A

$$t = \sqrt{\frac{2h}{g}}$$

where gravitational acceleration $g=981\pm 1$ cm s$^{-2}$.

Horizontal component of the acceleration of the ball $a_x=?$

The unchanging horizontal velocity of the ball $v_x = s/t$.

Vertical velocity of the ball just before it hits the table at point A $v_y = gt = -\sqrt{2gh}$.

The time the ball takes to reach point B from point A $t_{AB} = (s'-s)/v_x$.

Vertical component of the velocity of the ball after it leaves point A $v_y' = g t_{AB} / 2$.

Net velocity of the ball before it impacts at A $v = \sqrt{v_x^2+v_y^2}$.

Net velocity of the ball after it impacts at A $v' = \sqrt{v_x^2+v_y'^2}$.

Maximum height the ball reaches between points A and B

$$h' = \frac{g}{2}\left(\frac{t_{AB}}{2}\right)^2.$$

The angle of the trajectory before reaching A

$$\theta = \arctan{\frac{v_y}{v_x}}$$

and after leaving A

$$\theta' = \arctan{\frac{v_y'}{v_x}}.$$

Kinetic energy of the ball before collision at point A

$$E = \frac{1}{2} mv^2.$$

Kinetic energy of the ball after collision at point A

$$E' = \frac{1}{2} mv'^2.$$

Vertical component of the momentum before reaching A $P_y=mv_y$ and after leaving A $P'_y = mv'_y$.

Horizontal component of the momentum before reaching A $P_x=mv_x$.

Net momentum before reaching A $p = mv$.

Net momentum after leaving A $p' = mv'$.

Vertical component of the impulse imparted on the ball by the table $J_y = p_y - p'_y$.

Horizontal component of the impulse imparted on the ball by the table $J_x = p_x - p'_x$.