Solve Romeo's Pebble Problem: Hitting Juliet's Window

  • Thread starter SnowOwl18
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In summary: Anyway, thanks for the input!In summary, Romeo is trying to hit Juliet's window with pebbles as gently as possible. He is located 7.70m below the window, 8.90m from the wall, and the pebbles are going at a speed of 8.9m/s when they hit the window. The final answer to how long it takes for the pebbles to reach the window is 8.018s.
  • #1
SnowOwl18
71
0
I posted this the other day, but I only got one response from someone that was a reminder that the pebble would be following a parabolic path...but what need help with is going about solving the problem...here's the problem and what I tried again..sorry to post the same problem again, but I thought maybe with all the posts no one saw it. Any help would be awesome :eek:)

*Romeo is chucking pebbles as gently as he can up to Juliet's window. That is, he wants the pebbles to hit the window with the least possible speed...He is standing at the edge of a rose garden at H = 7.70m below her window and at D = 8.90m from the base of the wall. How fast are the pebbles going when they hit her window?*

Ok, so the horizontal component is 8.9m and the vertical is 7.7m...I tried
- tan= 7.7/8.9 to get theta and then use that to get the hypoteneuse, but i realized, after getting the problem wrong, that I only got the distance of the hypoteneuse, when i really needed the velocity...so how would i find that? thanks for any help
 
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  • #2
Draw a picture, and review projectile motion.
 
  • #3
Yes, that person who told you about the parabolic path was me. I also tried to get you to identify the point at which the speed would be the smallest, which is the summit of its trajectory (because at that point the pebble has no vertical speed). You have the vertical distance, the final vertical velocity, and the acceleration due to gravity, so can you find how long it takes to reach Juliet's window? From there you should be able to find the final answer.
 
  • #4
do you go to MIT?
 
  • #5
No, umm...why?
 
  • #6
no, the original poster. this was on the problem set for the freshmen and i noticed the original poster was from massachusetts.
 
  • #7
Surprising. This seems a little too basic for MIT standards.
 
  • #8
k thanks, I will try that :eek:) Nope, I go to the University of Michigan at Ann Arbor...the questions are easy because it's an algebra based physics class
 
  • #9
yeah, it is. well, it is the first pset, and it is for 8.01. 8.012, the more advanced version, uses kleppner amd kolenkow. i think this is from giancoli or somethin similar.
 

FAQ: Solve Romeo's Pebble Problem: Hitting Juliet's Window

1. How do you solve Romeo's pebble problem?

To solve Romeo's pebble problem, you will need to use the equation for projectile motion to calculate the angle and velocity at which the pebble should be thrown in order to hit Juliet's window. This equation takes into account the initial velocity, acceleration due to gravity, and the distance between Romeo and Juliet's window.

2. What is projectile motion?

Projectile motion is the motion of an object that is thrown or launched into the air and moves under the influence of gravity. It follows a curved path, known as a parabola, and can be described by the equation: y = y0 + xtanθ - (gx^2)/(2v0^2cos^2θ), where y0 is the initial height, x is the horizontal distance, θ is the angle of launch, g is the acceleration due to gravity, and v0 is the initial velocity.

3. What factors affect the trajectory of the pebble?

The trajectory of the pebble is affected by the initial velocity at which it is thrown, the angle at which it is thrown, and the acceleration due to gravity. The distance between Romeo and Juliet's window also plays a role in determining the trajectory.

4. How do you calculate the angle and velocity for the pebble to hit Juliet's window?

To calculate the angle and velocity, you will need to use the projectile motion equation and plug in the known values, such as the initial height, horizontal distance, and acceleration due to gravity. Then, you can rearrange the equation to solve for the angle and velocity. Alternatively, you can use a projectile motion calculator to get the desired values.

5. Are there any limitations to this approach?

Yes, there are a few limitations to this approach. Firstly, it assumes that the pebble is thrown with a constant velocity and that there are no external factors, such as wind, that could affect its motion. Additionally, the equation for projectile motion is based on the idealized conditions and does not take into account air resistance or the shape of the object being thrown. Therefore, the calculated angle and velocity may not be entirely accurate in real-world situations.

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