Introductory Physics I - PHYS 200 -Lab 3 NEW COMPLETE SOLUTION ATHABASCA COMPLETE UPDATE

Introduction: Projectile motion involves uniform horizontal motion combined with a downward acceleration due to gravity, resulting in a parabolic trajectory. Objects in projectile motion experience two simultaneous, yet independent, motions along the x and y axes. The horizontal component of the motion has zero acceleration and moves at a constant velocity. In contrast, the vertical component of the motion experiences a constant acceleration due to gravity (ay=−9.80 m/s^2).

By using Tracker software and kinematic equations, one can analyze this physical motion, collect data, and describe the results accurately.

Procedure: A measure tape was secured to the wall measuring 1.5m in height.

Starting between 50cm and 100cm away on the left from the measuring tape, the ball was thrown at an angle above the horizontal in order to show the full curve until it hits the ground again.

After the video was recorded, it was uploaded to Tracker to be analysed. The time was set at 0 seconds when the ball was about to leave the hand. The x and y axis were adjusted to both be at zero at the center of the ball before it left the hand. The length scale was then set to 1.5m representing the known length of the measuring tape within the video. Then I began to record data points collected at the center of the ball at each frame until the ball hit the ground measuring both x and y data points.

Once all of the data points were collected two graphs were created, x (horizontal position) vs. t (time) and y (vertical position) vs. t (time).

The graphical relation between the horizontal position and time created a linear graph and fit the

form of x=At+B. The graphical relation between the vertical position and time created a parabola and the best fit of form is y=At^2+Bt+C.

Pictures:

Data:

Analysis and Discussion:

When analyzing the motion of a projectile there are separate equations for both horizontal (x) and vertical (y) directions. For horizontal motion the equation is x ( t )=x0 + v x t where x0 is the initial horizontal position (along x axis) and v x is the constant horizonal 1

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velocity. For vertical motion the equation is y ( t )= y 0 + v y t − g t where 2 y0 is the initial position along the y-axis, v y is the initial vertical velocity,

and g represents acceleration due to gravity (-9.8m/s2) For horizontal motion the equation given from tracker is x=1.706t1.508. To determine if the ball moves with a constant velocity in the horizontal direction we check if the data points fit well to the linear model, and the velocity should remain constant, which Tracker calculated the slope to be a constant 1.71m/s.

To determine if the ball moves with constant acceleration we have been given we check the parabola with the equation y ( t )= y 0 + v t − 1g t 2 which you can see with the data points fit well y

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suggesting the acceleration is constant. Uncertainties: • Air resistance could have altered the ball’s trajectory

• Measurements could be inaccurate, starting time, placement, measuring tape calibration

Conclusion: By investigating the horizontal and vertical components of the ball’s trajectory, we were able to determine whether the ball moves with constant acceleration vertically and constant velocity horizontally. In the analysis of the vertical motion, it was 1

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compared to y ( t )= y 0 + v y t − g2t where the fit was good, which confirms the ball experienced constant acceleration as predicted. The horizontal analysis of the position vs. time data fit well against the linear model x ( t )=x0 + v x t and the slope of the line was consistent throughout the experiment supporting the ball moving at a constant velocity in the horizontal direction.

Questions: 1. Based on your best-fit analysis of your projectile motion, determine the acceleration due to gravity.

Assuming -3.840m/s^2 2. Estimate the ball’s horizontal velocity (𝑣𝑥) during flight.

Assuming 1.71m/s