# 1D & 2D Kinematics, Optics Questions

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.