("counting minima of two coherent sources.") this problem is an extension of the example of two coherent sources we discussed in class. two coherent point sources (let us call them s1 and s2) emit identical radio waves in phase at wavelength λ. s1 is positioned at (0, −d/2) and s2 is at (0, +d/2). a radio detector is placed very far away (compared to d) and can move on a large circle with respect to the coordinate origin and scan the interference pattern from the combination of waves from both sources.

(a) the radio detector is receiving the waves from both sources at angle θ with respect to +x-axis. what is the difference in path length, ∆l, between the waves coming from the two sources?

(b) given path difference ∆l, what is the phase difference at the detector?

(c) when the detector is on the x axis (both positive and negative), is it observing a minimum, or a maximum?

(d) the detector scans the full circle, and finds 30 points of zero intensity (minima), including two on the y-axis, one of them above the sources and the other one below the sources. what is the value of d/λ?

Abaseball picther can throw a ball at about 90 miles per hour, v = 40 m/s, on solid rock ground. we now put him into space. when he throws the ball, which weighs mb = 0.15 kg moves away from himat the same speed. how long does it take the ball thrown in space to travel the 30 meters to the batter? he weighs mp = 100kg

Jason and mia are both running in a race. as they approach the finish line, you being the physicist that you are decide to time how long it takes them to reach the end of the race. when you start your stop watch (you can take this as time t = 0 s) you notice that mia is an unknown distance d ahead of jason and both are moving with the same initial velocity v_0. you also notice that jason is accelerating at a constant rate of a_j, while mia is deaccelerating at a constant rate of -a_m. jason and mia meet each other for the first time at time t = t_1. at this time (t = t_1) jason's velocity is two times that of mia's velocity, meaning v_j (t_1) = 2v_m (t_1). a) draw the position vs. time graph describing mia's and jason's motion from time t = 0 to time t = t_1. clearly label your axes and initial conditions on your graph. b) draw the velocity vs. time graph describing mia and jason's motion from time t = 0s to time t = t_1. clearly label your axes and initial conditions on your graph. c) how long from when the stop watch was started at t = 0s did it take mia and jason to meet? express your answer in terms of know quantities v_0, a_m, and a_j. d) when the stop watch started at time t = 0s, how far apart, d, were mia and jason? express your answer in terms of know quantities v_0, a_m, and a_j.

Abicycle slows down when the rider applies the brakes. what type of energy transformation is involved in this example? a. kinetic energy into heat energy b. heat energy into potential energy c. potential energy into kinetic energy d. kinetic energy into mechanical energy