Harmonic oscillator (25 marks): consider a linear harmonic oscillator with the solution de- fined by the ladder operators a and a defined in class. use the number basis in) to do the following. class. use the nuim such that (ψ x1) is as large as a) construct a linear combination of 10) and 11) to form a state l possible. b) suppose that the oscillator is in the state constructed in a) at time t = 0, write an expression to de- scribe the time dependence of this state state for t > 0. evaluate the expectation value (t) x r(t)) as a function of time for t > 0. c) defining (δ2p = (t)lx? it((t)x1r(t))2. calculate (ar)2

A250-n box is at rest on a frictionless horizotal floor. then a person shoves the box with a non-zero force of magnitude p. which statement best describes the relationship betweeen p and the motion of the box after it was shoved? -the box will not move when p< 250n but otherwise will accelerate at a constant rate that is directly proportional to p - the box will begin moving at a speed that is directly proportional to p, then will gradually slow to a halt -the box will move with constant velocity at a speed that is directly proportional to p -box will accelerate across the floor at a constant rate that is directly proportional to p

Lacie kicks a football from ground level at a velocity of 13.9 m/s and at an angle of 25.0° to the ground. how long will the ball be in the air before it lands? how far will the football travel before it lands?

According to newton’s law of universal gravitation, which statements are true? as we move to higher altitudes, the force of gravity on us decreases. as we move to higher altitudes, the force of gravity on us increases. as we gain mass, the force of gravity on us decreases. as we gain mass, the force of gravity on us increases. as we move faster, the force of gravity on us increases.