Distance travelled by a falling body

AI Thread Summary
The discussion centers on the interpretation of a question regarding the distance traveled by a falling body, with two potential answers: 34.3m or 9.8m. Participants agree that the question is poorly worded, leading to confusion about which answer is correct. The mathematical interpretation indicates that the distance covered during specific time intervals can lead to the conclusion that the answer could be zero if misinterpreted. Clarification is provided on how to calculate distances based on time intervals, emphasizing the importance of understanding the context of "seconds" in the problem. Overall, the conversation highlights the need for clearer phrasing in physics questions to avoid misinterpretation.
Bl4nk
Messages
6
Reaction score
0
Homework Statement
"For a freely falling body from rest, not counting air resistance or any frictional force, between the third and fourth second of time, it travels a distance of?"
What does the question mean?
a. Distance traveled in the 4th second.
or
b. The difference between the distances travelled in the 4th second and the 3rd second.
And why?
Relevant Equations
h = ut + 1/2gt^2
If (a) is correct, the answer would be 34.3m.
If (b) is correct, the answer would be 9.8m.
I want to know exactly which one is meant by the question and the reason behind that. Personally i think its a.
 
Physics news on Phys.org
Yes, it's a. I don’t see how you could read it as b. Though I do prefer your rewording.
 
  • Like
Likes Bl4nk and topsquark
haruspex said:
Yes, it's a. I don’t see how you could read it as b. Though I do prefer your rewording.
Apparently I couldn't make one of my friends understand that its the question asks for A and not B
 
Mathematically it asks for the distance ##d = \left| h(t=4 \mathrm{s}) - h(t=3 \mathrm{s}) \right|##
 
  • Like
Likes Bl4nk and topsquark
One could argue that the correct answer is zero. The wording of the question is atrocious.

The "third second" starts at ##t=2## and ends just prior to ##t=3##. The "fourth second" starts at ##t=3## and ends just prior to ##t=4##. Between the two intervals, zero time elapses and zero distance is traversed.

[The "first second" starts at ##t=0## of course].

Possibly the intent is that "first second" denotes the instant at which the object is released at ##t=0##.
Possibly the intent is that "first second" denotes the instant one second later at ##t=1##.

Three plausible readings is an indication of poor writing.
 
I agree with @DrClaude's interpretation. Yes, the statement could have been clearer, but it is clear to me that there is an assumed imaginary clock that starts when motion starts, as is usually the case. Then one counts ticks of the second hand, tick 1, tick 2, etc. and figures out distances ##d_1##, ##d_2##, etc. covered from one tick to the next. Thus, $$\begin{align} & d_1=\frac{1}{2}a(1~\mathrm{s})^2 - \frac{1}{2}a(0~\mathrm{s})^2\nonumber \\ & d_2=\frac{1}{2}a(2~\mathrm{s})^2-\frac{1}{2}a(1~\mathrm{s})^2=3d_1 \nonumber \\ & \dots \nonumber \\ & d_n=\frac{1}{2}a \left[n^2-(n-1)^2\right]\mathrm{s}^2= (2n-1)d_1~. \nonumber \end{align}$$
 
Thanks everyone for explaining this so elaborately. For real tysm ^w^. Helped a lot.
 
Back
Top