Planet a takes 1 year to go around its star at an average of 1 a. u. distance. planet b is 4 a. u. from the star. calculate how long planet b takes to orbit.

The de broglie relation λ=h/p can be rewritten in terms of the wave number k as p=kℏ. recall that wave number is defined by k=2π/λ. using the fact that λ=v/f, find the wave numbers k1 and k2 corresponding to frequencies f1 and f2. express your answer as two expressions

One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. you see that the patch of light seems to be a circular diffraction pattern. it appears that the central maximum is about 1 cm across and you estimate that the distance from the window shade to the wall is about 3 m. what is (a) the average wavelength of sunlight? (b) the diameter of the pinhole?

Apendulum has a mass of 1.5 kg and starts at a height of 0.4 m. if it is released from rest, how fast is it going when it reaches the lowest point of its path? acceleration due to gravity is g = 9.8 m/s2. a. 2.8 m/s b. 0 m/s c. 5.9 m/s d. 4.3 m/s