Trial physics problem #2

Here's the problem:

"Every once in a while a bird will get hit by a baseball during a baseball game. The longest home runs in baseball land about 500 feet (which is 152.4 meters) from home plate. If these balls leave the bat at a 45 degree angle to maximize their distance, what is the minimum safe height in meters for birds around baseball stadiums?"

Then follows a picture of a parabola with the height of the apex labeled H.

This question seems confusing to me since the answer that successfully answers the question is the value of H. This can be done w/ simple calculus, no physics whatsoever.

I think a more appropriate answer would be to solve for the speed of the ball at launch, recognizing that that energy could be applied in the vertical direction, utilize that to determine a maximum height of the ball if hit straight up. Note this solution actually uses some physics.

Alternatively, the problem could be restated to "what is the minimum safe height in meters for birds to avoid these home runs?" (or of course get rid of the 'bird' part completely)

#Physics

Note by Jeff Gates
8 years, 1 month ago

No vote yet
2 votes

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list
  • bulleted
  • list

1. numbered
2. list
  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai−1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 ∑i=13 \sum_{i=1}^3
\sin \theta sin⁡θ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Jeff,

It certainly can be done with calculus, once you realize that the trajectory of the ball is actually a parabola. The physics comes in only in determining the shape of the trajectory. From your text above, and correct me if I'm wrong, it appears that you looked at the picture and assumed that it was a parabola, which isn't quite justified - looking at a picture and assuming a particular mathematical form can be a little dangerous.

As an aside, you are absolutely correct that in general once you have the equation of motion for a particle, the physics part is over. Everything else is just math (usually solving a differential equation). But the physics to determine accurately what the equation of motion is can be complicated!

David Mattingly Staff - 8 years, 1 month ago
×

Problem Loading...

Note Loading...

Set Loading...