1. (75) My sailboat has an ultrasonic wind meter at the top of the mast to indicate wind direction d and wind speed vw. The unit also has (and needs) a barometer, a hygrometer, and thermometer since the speed of sound depends on pressure, humidity and temperature. The ultrasonic portion of the sensor involves three sender/receiver pairs arranged in an equilateral triangle so that the transit time for a sound pulse is measured along the three sides of the triangle many times per second. A picture of the sensor with black sender/receiver pairs shown. When mounted on the mast, one vertex of the equilateral triangle faces the bow of the boat (or is pointing in the direction the boat is pointing). Wind angles on a sailboat are measured clockwise starting from that forward direction. So if wind is coming directly inward from the forward direction, the wind angle d =0. Wind directly from the right side (starboard side) is at 0 = 90", and so on. Find mathematical relations for the three clockwise (as seen from the sky) transit times for sound pulses along the sides of the triangle. Call them t1, t2, ts starting from the side starting at the vertex facing the bow. Show those time expressions in terms of d, Us, Up, 0. Plug in to find values for vs = 340", var = 10, 0 = 60", d = 0.120m