A steel ball is dropped from a diving platform (with an initial velocity of zero). Use the approximate value of g = 10 m/s2.

(a) Through what distance does the ball fall in the first 1.5 seconds of its flight?


(b) How far does it fall in the first 4 seconds of its flight?

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To solve these problems, we can use the equation of motion for an object in free fall:

(d) š‘‘ = 1/2š‘”š‘”Ā²

where š‘‘ is the distance, š‘” is the acceleration due to gravity (10 m/sĀ²), and š‘” is the time.

(a) To find the distance the ball falls in the first 1.5 seconds, we substitute š‘” = 1.5 into the equation:

š‘‘ = 1/2 * 10 * (1.5)Ā²
š‘‘ = 1/2 * 10 * 2.25
š‘‘ = 11.25 meters

Therefore, the ball falls approximately 11.25 meters in the first 1.5 seconds of its flight.

(b) To find the distance the ball falls in the first 4 seconds, we substitute š‘” = 4 into the equation:

š‘‘ = 1/2 * 10 * (4)Ā²
š‘‘ = 1/2 * 10 * 16
š‘‘ = 80 meters

Therefore, the ball falls approximately 80 meters in the first 4 seconds of its flight.

To find the distance the ball falls, we can use the equation for the distance traveled by a falling object in free fall:

š‘‘ = (1/2)š‘”š‘”Ā²

Where:
- š‘‘ is the distance traveled
- š‘” is the acceleration due to gravity (approximately 10 m/sĀ²)
- š‘” is the time

(a) Through what distance does the ball fall in the first 1.5 seconds of its flight?

Substituting the given values into the equation, we have:

š‘‘ = (1/2)(10)(1.5)Ā²
š‘‘ = 11.25 meters

Therefore, the ball falls approximately 11.25 meters in the first 1.5 seconds of its flight.

(b) How far does it fall in the first 4 seconds of its flight?

Using the same equation, we can evaluate:

š‘‘ = (1/2)(10)(4)Ā²
š‘‘ = 80 meters

The ball falls approximately 80 meters in the first 4 seconds of its flight.