So far, I’ve learned a lot in and really enjoyed physics, but that has definitely come with making a lot of mistakes on the way. This is one of many errors made along the way.
This question is found in the Kinematics 2 Review, being question #24.
While riding on an amusement park ride, you drop an object. The cart you were riding on at the time of the drop was rising vertically at a velocity of 11.0 m/s and was 5.0 m above the ground. How long does it take for the object to reach the ground?
My original solution:
Clearly, a few things went wrong here, but that’s not to discredit those that were correct.
I correctly stated my known and unknown values, although the distance ended up causing me trouble. I also had the right idea in using the quadratic equation to solve for time without needing to solve for final velocity and choosing the positive x value as my final answer.
The large error was in the labelling of the distance, understanding that since my velocity was positive and it was going up, the distance should also be positive as it was measured in the same direction. Because I wanted to try out using the quadratic equation to solve one of these questions, I actually ended up with a negative discriminant due to the distance value being positive. At the time, I did not understand why that value shouldn’t be positive, but blissfully changed it to make my equation work out. Unfortunately, I had forgotten to write down the negative in the denominator, so even this solution was incorrect.
In reality, the distance should be negative. This is because it is not the distance being travelled by the object in between the initial and final velocities (or in the time period being measured), but the distance it needs to travel down during the time period being measured. Since we consider down to be negative, that is what this value needs to be. This could have been easier to notice had I considered the 5.0 m to be not distance, but displacement, forcing myself to think about which direction it is in.
Analyzing this question has taught me to better visualize and understand what the information given is actually telling me. A lot of the times, values will need to be properly interpreted before they can be used in formulas, and this was a great example to learn this from. Reflecting back to the Kinematics 2 Skills Check, the question involving a seagull passing under a falling ball is similar, in the sense that displacement easily become confusing. Stepping back, drawing diagrams, and properly interpreting the information can prevent similar errors.
The correct solution can be obtained in 2 ways: through finding the final velocity first, then using it to find time, or directly finding time through the quadratic equation.
To explain the process for answering this question (for a grade 10 student), I will be following solution #1, as the quadratic equation is much less intuitive, and frankly, a lot more difficult.
Although step 6 could be optional, I find it has allowed me to catch an incorrect solution before looking at the answer key, and is good practice for tests.
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