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 = 1/2šš”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)šš”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.