Solve Monkey Dropping Coconut Problem on a Sunny Day

  • Thread starter bukky
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In summary, the problem involves finding the height from which a monkey dropped a coconut based on the time it takes for the sound of the coconut hitting the ground to reach the listener, the angle at which the listener is viewing the monkey, and the speed of sound. The formula used is y = 4.9t^2, and the distance from the tree is x = y/(tan 5). The question can be approached by using the formula v1-vo = 2ax and solving for t, keeping in mind that the time for sound to reach the listener is 1.90 times longer than the time for the coconut to fall.
  • #1
bukky
5
0
Hi,
I just joined today and would like help with a question. Here it is:

It is a sunny day and you are lying on a beach . Some distance away across level gropund, is a tall coconut palm. As you watch, a monkey in that tree drops a coconut(from rest) onto hard ground below. The time elapsed from the moment he releases the coconut until it hits the pavement is 190% longer than the time it takes for the impact to reach you. The angle (measured with respect to the ground ) at which you are viewing the monkey when he drops the nut is 5 degrees. Assumimg the speed of sound is constant 343m/s, from what height did the monkey drop the nut?
Thanks
 
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  • #2
time for sound to reach you = (1.90t + t) =2.90t
time for coconut to fall = t
height of tree = y
distance from tree = x = y/(tan 5)
 
  • #3
bukky, if this is homework or course work you should show us what you have tried on this. (If it isn't, this is the wrong forum.)

Chi Meson, did you misread the question? Bukky said ". The time elapsed from the moment he releases the coconut until it hits the pavement is 190% longer than the time it takes for the impact to reach you." (I presume the "impact" is the sound of the coconut hitting the pavement.) You say "time for sound to reach you = (1.90t + t) =2.90t". If t is the time it takes for the coconut to hit the ground, then the time for the sound to reach you is t/1.90.
Letting x be the horizontal distance to the bottom of the tree (where the coconut hits) then x= 343t/1.9= 180.5t. Letting y be the height of the tree, then y= 4.9t2. You can solve
tan(5)= y/x= (4.9/180.5)t= 0.027t for t and then find y.
 
  • #4
HallsofIvy said:
bukky, if this is homework or course work you should show us what you have tried on this. (If it isn't, this is the wrong forum.)

Chi Meson, did you misread the question? Bukky said ". The time elapsed from the moment he releases the coconut until it hits the pavement is 190% longer than the time it takes for the impact to reach you." (I presume the "impact" is the sound of the coconut hitting the pavement.) You say "time for sound to reach you = (1.90t + t) =2.90t". If t is the time it takes for the coconut to hit the ground, then the time for the sound to reach you is t/1.90.
Letting x be the horizontal distance to the bottom of the tree (where the coconut hits) then x= 343t/1.9= 180.5t. Letting y be the height of the tree, then y= 4.9t2. You can solve
tan(5)= y/x= (4.9/180.5)t= 0.027t for t and then find y.

It is an assignment and we were( class) given any hunts on how to solve the problem.
I have attempted the problem numerous times. I was using the formula
v1-vo=2ax. I do have a question? how did you obtain 4.9t? is there a formula I could use to approach such a question in the future? I want to make sure I understand it. Rather than just obtaining the answer.
Thanks for your help
 
  • #5
Chi Meson said:
time for sound to reach you = (1.90t + t) =2.90t
time for coconut to fall = t
height of tree = y
distance from tree = x = y/(tan 5)
Thanks for your help!
 

1. How does the "Monkey Dropping Coconut Problem" relate to science?

The "Monkey Dropping Coconut Problem" is a classic example in physics that demonstrates the principles of projectile motion. It involves a monkey on top of a tree dropping a coconut at the same time a hunter fires a bullet at the monkey. This problem helps us understand the relationship between time, distance, and acceleration in a real-world scenario.

2. What factors affect the outcome of the "Monkey Dropping Coconut Problem"?

The outcome of the "Monkey Dropping Coconut Problem" is affected by several factors, including the initial height of the monkey and the coconut, the initial velocity of the coconut, the angle at which the hunter fires the bullet, and the acceleration due to gravity. These factors all play a role in determining the trajectory and landing point of the coconut.

3. How can we solve the "Monkey Dropping Coconut Problem" using scientific principles?

To solve the "Monkey Dropping Coconut Problem", we can use the equations of motion and principles of projectile motion. By breaking down the problem into smaller components and using mathematical equations, we can calculate the time, distance, and velocity of the coconut and the bullet. This allows us to determine whether the coconut will hit the hunter or not.

4. Is the "Monkey Dropping Coconut Problem" a realistic scenario?

The "Monkey Dropping Coconut Problem" is a hypothetical scenario used to illustrate the principles of projectile motion. While it may not be a common occurrence in real life, it helps us understand and apply scientific concepts to practical problems. The scenario may also vary based on different factors such as air resistance and the weight and shape of the coconut.

5. What other real-world applications can be derived from the "Monkey Dropping Coconut Problem"?

The "Monkey Dropping Coconut Problem" has many practical applications, such as predicting the trajectory of a projectile in sports like baseball or golf, estimating the landing point of a missile or rocket, and understanding the motion of objects in space. It also helps us understand how factors such as air resistance and wind can affect the trajectory of a projectile.

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