The amount of time in seconds it takes for a swimmer to hear a single, hand-held, starting signal is given by the formula

where (x, y) is the location of the starter (in meters), (0, p) is the location of the swimmer (in meters), and C is the air temperature (in degrees Celsius). Assume that the starter is located at the point (x, y) = (5, -2). See the diagram on the next page.

(a) Calculate t(5, -2, 20, 20) and t(5, -2, 10, 20). Could the difference in time change the outcome of a race?
(b) Calculate the total differential for t if the starter remains stationary, the swimmer moves from 20 m to 20.5 m away from the starter in the y direction, and the temperature decreases from 20°C to 15°C. Interpret your answer.

Transcribed Image Text:

t(x, y, p, C) = √x² + (x − p)² 331.45 + 0.6C