Solving a Gr. 11 Physics Assignment: Finding Vertical Displacement of a Potato

[Gombay]

I have to find the vertical displacement of a potato shot out of a potato launcher (Gr. 11 Physics assignment). It would make sense (and make this easier) to assume that the potato went straight up and down and I am allowed to assume that air resistance is negligible. My main problem is proving algebraically that the upward motion and downward motion are equal in terms of time. If they aren't equal I guess I need to start my thinking all over. :uhh: Here are my givens if they are needed:
m = 249g
Δt = 4.15s

Any help would be appreciated. Thanks.

 

[rockerdoctor]

This problem is based around gravity. Think about how gravity affects the rate of any falling object. Also, remember the acceleration of gravity is a constant. So we can assume it will decelerate going up the same rate it accelerates falling back down, meaning the time it takes to go up=time it takes to fall (4.15s). We know that if we start at the top and let it fall the initial velocity is 0, the acceleration downwards is gravity or 9.8m/s^2, and we know it takes 4.15s to fall. If you have the right formula, those numbers will give you the answer. Think of the formula that incorporates constant acceleration, time, and displacement.

 

[Moetasim]

I would first like to commend you for taking on this challenging physics assignment. It is important to approach problems like this with a critical and analytical mindset, and your willingness to seek help and clarification shows great scientific thinking.

To solve this problem, we can use the basic equation for displacement, which is Δx = v0t + 1/2at^2, where Δx is the displacement, v0 is the initial velocity, t is the time, and a is the acceleration.

In this case, we can assume that the initial velocity of the potato is 0, since it is being shot straight up and down. We also know that the acceleration due to gravity is -9.8 m/s^2, since the potato is being pulled down by the force of gravity.

Therefore, the equation becomes: Δx = 0 + 1/2(-9.8)(4.15)^2 = -85.3 cm. This means that the vertical displacement of the potato is 85.3 cm downwards.

To prove that the upward and downward motions are equal in terms of time, we can use the equation for time of flight, which is t = √(2Δx/a), where t is the time, Δx is the displacement, and a is the acceleration.

In this case, we can plug in the values we know: t = √(2(-85.3)/(-9.8)) = 4.15 s. This shows that the time for the upward motion is equal to the time for the downward motion, as expected.

In conclusion, by using the basic equations for displacement and time of flight, we can solve for the vertical displacement of the potato and prove that the upward and downward motions are equal in terms of time. However, it is important to note that in real world scenarios, air resistance may affect the motion of the potato and should be taken into consideration for more accurate results. I hope this helps and good luck with your assignment!