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Multiple Choice
What is the depth of the lake if a lead ball is dropped from a diving board 5.70 m above the water and reaches the bottom 3.70 s after it is released, assuming it sinks with a constant velocity equal to the velocity with which it hit the water?
A
12.15 m
B
8.45 m
C
15.00 m
D
10.00 m
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Verified step by step guidance
1
First, calculate the velocity of the lead ball as it hits the water. Use the kinematic equation for free fall: , where is the initial velocity (0 m/s, since it is dropped), is the acceleration due to gravity (approximately 9.81 m/s²), and is the time taken to hit the water.
Calculate the time taken to hit the water using the equation , where is the distance fallen (5.70 m). Solve for .
Once you have the time to hit the water, subtract it from the total time (3.70 s) to find the time the ball spends sinking in the water.
Use the constant velocity calculated in step 1 to find the depth of the lake. Since the velocity is constant, use the equation , where is the depth of the lake, is the velocity, and is the time spent sinking.
Add the depth calculated in step 4 to the initial height of the diving board (5.70 m) to find the total depth of the lake.