Apendulum consists of a stone with mass m swinging on a string of length l and negligible mass. the stone has a speed of v0 when it passes its lowest point. (a) write an expression for the speed of the stone when the string is at some angle theta with the vertical. (b) what is the greatest angle with the vertical that the string will reach during the stone's motion? (c) if the potential energy of the pendulum-earth system is taken to be zero at the stone's lowest point, what is the total mechanical energy of the system? state all your answers in terms of the given variables and g.

Afigure skater is rotating at a rate of 200 revolutions per minute. what is the angular speed, in units of rad/s? 20.9 12000 200 3.33

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?

Light from two different sources are incident upon the same side of a polarizing filter. light from one source is polarized with total intensity ip, while light from the other source is unpolarized with total intensity iu. as you rotate the polarizing filter through 360 degrees, the intensity of the transmitted light on the other side varies by a factor of 9. what is the relative intensity of the initial polarized source to the unpolarized source, or ip/iu?