The acceleration of a rocket traveling upward is given by a =(6 + 0.02s)m/s², where s is in meters. Determine the time needed for the rocket to reach an altitude of s =100m. Initially, v=0 and s= 0 when t = 0.

II) A high-speed drill reaches 2000 rpm in 0.50 s. ! What is the drill's angular acceleration? Through how many revolutions does it turn during this first0.50 s?

In one type of computer keyboard, each key holds a small metal plate that serves as one plate of a parallel-plate, air-filled capacitor. When the key is depressed, the plate separation decreases and the capacitance increases. Electronic circuitry detects the change in capacitance and thus detects that the key has been pressed. In one particular keyboard,the area of each metal plate is 44.5 mm, and the separation between the plates is 0.71n mm before the key is depressed. Calculate the capacitance before the key is depressed. If the circuitry can detect a change in capacitance of 0.300 pF, how far must the key be depressed before the circuitrydetects its depression?

In the figure the four particles are fixed in place and have charges q1, = 97 = 3e, 93 = 2e, and 94 = -8e. Distance d = 3.55 um. What is the magnitude of the net electric field at point P due to the particles?

An observer O notes that two events are separated in space and time by 600 m and 8 x 10 s, respectively. How fast must an observer O' be moving relative to O in order that the events seem simultaneous?

Problem 17. A spool of wire of mass M and radius R is unwound under a constant force F.Assume that the spool is a uniform solid cylinder that doesn't slip. (a) Find the acceleration of the center of mass. Hint: You should apply Newton's 2nd Law for rotation about an axis through the contact point with the horizontal surface. (b) In this particular problem, it is actually unclear which direction the static friction force points in. Explain why this is the case. (c) Find the magnitude and direction of the static friction force. (d) If the cylinder starts from rest and rolls without slipping,what is the speed of its center of mass after it has rolled through a distance d? You may assume that the mass of the wire is much less than the mass of the spool and therefore you can ignore the change in mass as the spool unwinds.

Problem 9. A particle of mass m slides without friction inside a hemispherical bowl of radius R.Show that if the particle starts from rest with a small angular displacement from equilibrium, it moves in simple harmonic motion with an angular frequency equal to that of a simple pendulum of length R. Use the angular position 0 shown in the diagram.

0.15-m-diameter pulley turns a belt rotating the driveshaft of a power plant pump. The torque applied by the belt on the pulley is 200 N - m, and the power transmitted is 7 kW. Determine the net force applied by the belt on the pulley, in kN, and the rotational speed of the driveshaft, in RPM.

In the following diagram the bottom block is being pulled downward with a force of 15 N. Calculate the tension in rope A if the mass of the top block is 2.0 kg and the mass of the bottom block is 5.0 kg. (3 marks)

A 30.0-kg gun is standing on a frictionless surface. The gun fires a50.0-g bullet with a muzzle velocity of 310 m/s. a) Calculate the momenta of the bulletand the gun after the gun was fired. b) Calculate the kinetic energy of boththe bullet and the gun just after firing.