Related Rates Help with physics?
A lifeguard standing on a tower throws a buoy to a swimmer than 18 m from the tower. The lifeguard, located 3 meters water, pull on the rope at a speed of 1 m / s. (a) How fast are the swimmer to reach the shore when is 15 meters from the water's edge, (b) How fast are the swimmer come when 3 m of the water's edge?
Sketch of the situation and find that: the length of the tow line extended to the rescuer swimmer standing on the top of the tower is given by the Pythagorean theorem: c = √ (3 ² + 18 ²) = 18,248 m strip the lifeline of the swimmers the distance x from the coast ranges, in particular, x is small. c ² = 3 ² + x ², so x = √ (c ² – 3 ²), now, by the chain rule for differentiation: dx / dt = (dx / dc) (dc / dt) = ½ [2c / √ (C ² - 3 ²)] (dc / Dt) dx / dt = [c / √ (c ² - 3 ²)] (dc / dt) = [c / x] dc / dt, but dc / = 1 m / s, c = 18.248 m, and Part a) x = 15 m for Therefore, dx / dt = (18.248/15) (1) = 1.2165 m / s, and for Part B): dx / dt = (18.248 / 3) (1) = 6.082 m / s,
Super Mario Galaxy Playthrough Part 18- Buoy Base Galaxy
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