1. Trajectory of a projectile

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.

1. Introduction and Theory

A projectile

2. Experimental Setup

List of apparatus: table, bench, ramp, marble ball, recording paper, carbon paper, adhesive tape, long meter scale, short meter scale, weight scale.

3. Method and Data

Quantity	Symbol	Value	Error ($\delta$)
Height of the release point	$H$	$11$ cm	$\delta H$ = 0.1 cm
Height of the end of the ramp	$h$	cm	$\delta h = $ cm
Height of the second bounce	$h'$	cm	$\delta h' = $ cm
Position of the first bounce	$s$	cm	$\delta s=$ cm
Position of the second bounce	$s'$	cm	$\delta s'=$ cm
Mass of the marble ball	$m$	cm	$\delta m=$ g

4. Analysis and Results

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

4.1 Time and velocity

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 $v' = \sqrt{v_x^2+v_y'^2}$.

4.2 Angle and height

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

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

4.3 Kinetic energy

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

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

4.4 Momentum

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 $p' = mv'$.

4.5 Impulse

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 $J_x = p_x - p'_x$.

Abekta

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