Neglect the diameters of the small pulleys and establish the relationship between the velocity of A and the velocity of B for a given value of y. If b = 1.30 m, y = 0.58 m, and vA = 1.65 m/s downward, what is the velocity of B (positive if downward, negative if upward).

This question is similar to the question above but read and calculate carefully. The situation has changed and the numbers have changed. Bonita Cart Bonita is again pulling a cart to the right. The cart used to be tied to a wall but now the rope has broken so the cart rolls over the horizontal floor without friction. Assume that the only forces on the cart are tension forces (including the force from Bonita), normal forces, and gravity with g = 9.81 m/s?. Bonita's shoes do not slide over the floor. Bonita has a mass of 52 kg. The cart has a mass of 45 kg. The mass of the rope is small enough to be ignored. Bonita is pulling the cart with a constant force of 283 newtons. Calculate the magnitude of the force that the cart exerts on Bonita. Note that the magnitude of a force is a positive quantity.

Provide complete solutions with the derivation of formulas integrals and derivatives

5. A simple pendulum at the UCR department of physics and astronomy has a length of 20 m, and the acceleration due to gravity at this location is measured to be 9.803 m/s². Calculate the period of the pendulum.

4. A stunt plane flying at the Reno Air Races is moving through the sky. The rectangular coordinates describing its motion are: x = -0.74t³ + 2.5t² + 10.25t y = -6.23t² + 16.45t + 8.94 where x and y are given in ft and t is given in seconds. a. Calculate the velocity vector, v, and acceleration, a, of the plane after 10 seconds (velocity is in ft/s and acceleration is in ft/s²). You may want to look back at your Topic 2 notes to recall how position, velocity, and acceleration are related. Your final answer should be given in vector form. b. Calculate the magnitude of the velocity (in mph) and the acceleration (in ft/s²) at t = 10 sec. [Ans. to Check: v = 132.46 mph; a = 41.32 ft/s²]