Couple of kinematics problems

In summary: The time interval from when the apple is dropped to when the photos are taken can be divided into two parts (t1 and t2) that add to give 3.4secs. What does each part mean? Can you find an equation for each one? Is there a variable that represents the diameter of the apple in each one?
  • #1
Phantom8295
2
0
Can anyone suggest how to do these problems.

1) A rocks is dropped from a sea cliff and the sound of it striking the ocean is heard 3.4s later. If the speed of sound is 340m/s, how high is the cliff?

2) An apple is dropped and a multi-flash camera is used to take photographs of the falling apple. If the apple is of 10c in diameter, estimate the time between each photoflash of the apple?

I got really stuck with these two problems. Any suggestions how to solve them?

Thanks
P.
 
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  • #2
Over on page 3 is a similar question entitled "Simple Problem: Depth of Well providing sound reaches you in 1.5 seconds" and Doc Al (one of the bigger of the Brains on PF) said how to do it, something about quadratics. Maybe you'll get lucky and he'll answer it again...

That second problem, I don't know at all. Guess you'll need to find its volume (it's sort of a sphere) and think of it falling down at the gravitational constant. Guess they want to have a clear shot of it each time?

Good luck, hope one of the Brains answers you.
 
  • #3
Let H be the height of the cliff. The function describing the rock's location is:

[tex]y_{(t)} = \frac{1}{2}gt^2[/tex]

From there you can find the time it takes the rock to reach the bottom of the cliff:

[tex]y_{(t = t_f)} = \frac{1}{2}gt_f^2 = H[/tex]

[tex]t_f = \sqrt{\frac{2H}{g}}[/tex]

Now, how much time does it take sound to travel a distance of H (from the bottom of the cliff to your ears) at a speed of 340m/s?

[tex]H = v_st_s[/tex]

[tex]t_s = \frac{H}{v_s}[/tex]

Finally, you know that the sum of these two time intervals should equal 3.4 seconds:

[tex]t_f + t_s = 3.4[/tex]

[tex]\sqrt{\frac{2H}{g}} + \frac{H}{v_s} = 3.4[/tex]

If you let [tex]x = \sqrt{H}[/tex] you get this equation:

[tex]\frac{x^2}{v_s} + x\sqrt{\frac{2}{g}} - 3.4 = 0[/tex]

Now solve for x and then find H. :smile: I get H = 51.7 meters.
 
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  • #4
thanks chen

I solved that problem.

As for the apple problem, its basically an apple is dropped and the photos are taken at regular intervals. The shot does not have to be a complete apple, as it falls down the acceleration increases and the distance between the previous position to current position increases at each shot. The questions is how many shots can be taken in a sec, or what's the time interval between each shot. Hope i am making it clear. I am still clueless about it. Have to try it again tomorrow. Have a good night folks.

P.
 
  • #5
That really depends on what kind of camera you're using, doesn't it?

You could program the camera to take pictures such that the distance between each image of the apple is the same, or you could take the pictures at a constant rate to see the acceleration.

What exactly is being asked?

cookiemonster
 
  • #6
They must want a clear shot of the apple each time. That's why they give a hint on its size. Since it's going to fall approx 5 m during the second, how many lengths of apple is that? That may be what they want.
 
  • #7
They want him to find the distance between r(0s) and r(1s)? Seems kinda easy...

cookiemonster
 
  • #8
:eek: E A S Y ? ? ? :eek:

Easy for whom? Yeah, for someone with a big ol' brain, maybe...
 
  • #9
1) A rocks is dropped from a sea cliff and the sound of it striking the ocean is heard 3.4s later. If the speed of sound is 340m/s, how high is the cliff?

Edit: Well I see Chen did your homework for you, so you don't need my help below. But you didn't learn anything either; nice work Chen! :wink:

The time interval from when the rock is dropped to when the sound is heard can be divided into two parts (t1 and t2) that add to give 3.4secs. What does each part mean? Can you find an equation for each one? Is there a variable that represents the height of the cliff in each one?

2) An apple is dropped and a multi-flash camera is used to take photographs of the falling apple. If the apple is of 10c in diameter, estimate the time between each photoflash of the apple?

Check the original wording of the problem; you're leaving something out.
 
Last edited:
  • #10
I have great confidence in phantom that he could solve such a problem. =]

cookiemonster
 

1. What is kinematics and why is it important?

Kinematics is the study of motion, specifically the position, velocity, and acceleration of objects without considering the forces that cause the motion. It is important because it helps us understand and predict the behavior of objects in motion, which is crucial in fields such as engineering, physics, and astronomy.

2. What are the different types of kinematics problems?

There are three main types of kinematics problems: constant acceleration, projectile motion, and circular motion. Constant acceleration problems involve objects that are accelerating at a constant rate, such as a car speeding up or slowing down. Projectile motion problems involve objects that are launched into the air and follow a curved path, such as a ball being thrown or a bullet fired from a gun. Circular motion problems involve objects that are moving in a circular path, such as a car going around a curve or a planet orbiting a star.

3. How do you solve a kinematics problem?

To solve a kinematics problem, you need to identify the given information and what you are trying to find. Then, you can use the equations of motion, such as the kinematic equations, to solve for the unknown variable. It is important to use consistent units and pay attention to the direction of motion when solving kinematics problems.

4. Can kinematics be applied to real-world situations?

Yes, kinematics can be applied to real-world situations. In fact, it is used in many fields to analyze and design systems and machines. For example, engineers use kinematics to design cars, airplanes, and other vehicles. Physicists use kinematics to study the motion of planets, stars, and other celestial bodies. And athletes use kinematics to improve their performance in sports.

5. What are some common misconceptions about kinematics?

One common misconception about kinematics is that it only applies to objects moving in a straight line. While this is true for constant acceleration problems, kinematics can also be applied to objects moving in curved paths, such as projectile motion and circular motion. Another misconception is that velocity and acceleration are the same thing. Velocity is the rate of change of an object's position, while acceleration is the rate of change of an object's velocity. They are related, but not the same.

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