1D & 2D Kinematics, Optics Questions

[bap902]

1. A ball is dropped of the top of a building whose height is d. The ball falls the last 2/3 of its distance in 3 seconds. What is the total time of its fall? What is the total distance of its fall?

I used this equation to start this problem.
http://img238.imageshack.us/my.php?image=physeqiw7.png

I put in -10 for acceleration and arrived at -3.3T²=-5(T-3)² from there, I got 1.7T² - 30T + 45=0 after distributing everything and moving it to one side. After that, I solved for T using the quadratic formula and got T = 16 sec. To find the total distance of the fall I used y=1/2gT² using -10 for g and 16 for T to get 1280 m.

2. What is the magnification of a pencil that is 10 cm from a convex mirror whose focal length is 8 cm?

For this problem, I started with m=d(image)/d(object). I knew the d(object) was 10 cm so I used 1/f = 1/d(object) + 1/d(image) using -8 for the f (because the focus is negative in a convex mirror) and 10 for the d(object). Doing this, I found that the d(image) was -4.4 and dividing that by 10 cm to find the magnification, I got -.4 for my answer.

3. http://img222.imageshack.us/my.php?image=physgrut3.png
Find the total distance, total displacement, and average velocity based on the graph.

For this problem, I found the area of the triangle based on 1/2bh and the area of the rectangle using bh. I found the area of the triangle to be 50 and the area of the rectangle to be 15. To find the distance, I added these two figures to get 75. To find the displacment, I subtracted these two figures to get 35. To find the displacement, I did v=d/t using 35 for the d and 15 seconds for the t. I got 2.3 as my answer.

 

[anathema]

Hi there,

I see that you have solved the problems using the appropriate equations and formulas. Your solution for the first problem is correct. The total time of the fall is 16 seconds and the total distance is 1280 meters.

For the second problem, you have correctly used the formula for magnification. However, the focal length of a convex mirror is always positive, so the value should be 8 cm instead of -8 cm. This would give a magnification of 0.4, not -0.4.

For the third problem, you have correctly calculated the distance and displacement. However, for average velocity, you need to use the total displacement, not just the displacement in one direction. Therefore, the average velocity would be 2.3 m/s, not 2.3 m/s in one direction.

Overall, your approach to solving these problems is correct. Just make sure to pay attention to the signs and units in your calculations. Keep up the good work!

 

[baba89]

I would like to point out that it is important to use the correct units in all calculations. In the first problem, the units for time should be in seconds, and in the third problem, the units for velocity should be in meters per second. It is also important to mention that the acceleration due to gravity, g, is usually given as -9.8 m/s², so it would be more accurate to use this value in the calculations. Additionally, it is important to show all steps of the calculations and provide units for all answers.

In the first problem, the total time of the fall is 4 seconds and the total distance of the fall is 160 meters. It would also be helpful to mention that the -10 for acceleration is due to the downwards direction of gravity.

In the second problem, the magnification should be written as -0.4, since it is a negative value. It would also be beneficial to explain the significance of the negative value in relation to a convex mirror.

In the third problem, it would be more accurate to use the trapezoidal rule to calculate the distance and displacement from the graph. The average velocity should also be calculated using the total displacement over the total time, which would give a value of 2.33 m/s. Additionally, it would be helpful to mention that the units for time in this problem are in seconds.

Overall, it is important to be thorough and precise in all scientific calculations and to use the correct units and values for accuracy.