3. 4 points SerCP9 5AE.005. My Notes Ask Your T EXAMPLE 5.5 Platform Diver GOAL

Question

3. 4 points SerCP9 5AE.005. My Notes Ask Your T EXAMPLE 5.5 Platform Diver GOAL Use conservation of energy to calculate the speed of a body falling straight down in the presence of gravity 10.0 m PROBLEM A diver of mass m drops from a board 10.0 m above the water's surface, as in the figure. Neglect air resistance. (a) Use conservation of mechanical energy to find his speed 5.00 m above the water's surface (b) Find his speed as he hits the water 5.00 m STRATEGY Refer to the problem-solving strategy. Step 1: The system consists of the diver and Earth. As the diver falls, only the force of gravity acts on him (neglecting air drag), so the mechanical energy of the system is conserved, and we can use conservation of energy for both parts (a) and (b). Step 2: Choose y 0 for the water's surface. Step 3: In part (a), y = 10.0 m and y = 5.00 m are the points of interest, while in part (b), y = 10.0 m and y = 0 m are of interest. SOLUTION (A) Find the diver's speed halfway down, at y 5.00 m. KE +PE KE+PE Step 4: We write the energy conservation equation and supply the proper terms + mgyt

Explanation / Answer

PRACTICE IT:

a) Using energy conservation,

PE +KE at top = PE + KE at 3m above water

(m x 9.8 x 6 ) + 0 = (m x 9.8 x 3) + (m x v^2 / 2)

v^2 /2 = 9.8 x (6-3)

v = 7.67 m/s

b) Using energy conservation,

PE +KE at top = PE + KE at surface of water

(m x 9.8 x 6 ) + 0 = (m x 9.8 x 0) + (m x v^2 / 2)

v^2 /2 = 9.8 x 6

v = 10.8 m/s

=-------------------------
Using energy conservation,

PE +KE at top = PE + KE at surface of water

(m x 9.8 x 6 ) + (m x 3.98^2 /2) = ( 0 ) + (m v^2 /2)

v^2 /2 = (9.8 x 6) + (3.98^2 / 2)

v = 11.55 m/s

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