Question

projectiles activity
part 1: air table
objective: use measurements of position over time to calculate the horizontal and vertical motion of a projectile.
do you predict that the horizontal velocity will increase, decrease, or stay constant over time?
do you predict that the vertical velocity will increase, decrease, or stay constant over time?
data and analysis
find the horizontal velocity, in terms of \boxes/tick.\ show your calculation or reasoning here. what is the horizontal acceleration?
find the vertical acceleration, in terms of \boxes/tick².\ show your calculation or reasoning here.
pick 8 - 10 points from the paper. on a separate sheet of graph paper, draw four graphs, for the horizontal position and horizontal velocity over time, and the vertical position and vertical velocity over time. staple it here.
do the horizontal motion graphs exhibit constant velocity or acceleration? explain, using the graphs as evidence.
do the vertical motion graphs exhibit constant velocity or acceleration? explain, using the graphs as evidence.

Explanation:

Step1: Predict horizontal velocity

In the absence of horizontal - forces (neglecting air - resistance on air table), the horizontal velocity of a projectile remains constant. So, the horizontal velocity will stay constant over time.

Step2: Predict vertical velocity

Under the influence of gravity, the vertical velocity of a projectile changes. Since the acceleration due to gravity acts downwards, the vertical velocity of a projectile in free - fall increases over time.

Step3: Calculate horizontal velocity

Let the horizontal displacement between two consecutive ticks be $\Delta x$ (in boxes). If the time interval between two consecutive ticks is $\Delta t$ (constant), the horizontal velocity $v_x=\frac{\Delta x}{\Delta t}$ (boxes/tick). Since there is no horizontal acceleration ($a_x = 0$), the horizontal velocity remains the same for all time intervals.

Step4: Calculate vertical acceleration

Let the vertical displacements at consecutive time intervals be $y_1,y_2,y_3,\cdots$. Using the kinematic equation $\Delta y=a_y\Delta t^2$ (where $\Delta y = y_{n + 1}-y_n$). We can find the vertical acceleration $a_y=\frac{\Delta y}{\Delta t^2}$ (boxes/tick²). In the presence of gravity, the vertical acceleration is non - zero and constant (assuming no air - resistance).

Step5: Analyze horizontal motion graphs

If the horizontal motion graph of position vs time is a straight line with a constant slope, it indicates a constant velocity ($v_x=\text{slope}$). If the horizontal velocity vs time graph is a horizontal line, it also indicates a constant velocity (since $a_x = 0$).

Step6: Analyze vertical motion graphs

The vertical position vs time graph is a parabola ($y = y_0+v_{0y}t+\frac{1}{2}a_y t^2$) which indicates a non - constant velocity (due to acceleration). The vertical velocity vs time graph is a straight line with a non - zero slope, indicating a non - zero constant acceleration ($a_y=\text{slope}$).

Answer:

Horizontal velocity prediction: stays constant.
Vertical velocity prediction: increases.
Horizontal velocity calculation: $v_x=\frac{\Delta x}{\Delta t}$ (boxes/tick), $a_x = 0$.
Vertical acceleration calculation: $a_y=\frac{\Delta y}{\Delta t^2}$ (boxes/tick²).
Horizontal motion graphs: exhibit constant velocity (straight - line position vs time graph with constant slope and horizontal velocity vs time graph).
Vertical motion graphs: exhibit constant acceleration (parabolic position vs time graph and straight - line velocity vs time graph with non - zero slope).