The stone fell in the air for 7 seconds and fell in the water for 5 seconds
Step-by-step explanation:
A stone fell from the top of a cliff into the ocean.
- In the air, it had an average speed of 16 m/s
- In the water, it had an average speed 3 m/s before hitting the seabed
- The total distance from the top of the cliff to the seabed is 127 meters
- The stone's entire fall took 12 seconds
We need to find how long the stone fell in the air and how long it
fell in the water
Assume that the time that the stone took to fall in the air is x
Assume that the time that the stone took to fall in the water is y
∵ Distance = speed × time
∵ The stone fell in the air by an average speed 16 m/s
∵ The stone took x seconds to fill in the air
∴ The distance in the air = 16 x
∵ The stone fell in the water by an average speed 3 m/s
∵ The stone took y seconds to fill in the water
∴ The distance in the water = 3 x
Add the distance in the air and the distance in the water to find
the total distance
∵ The total distance that the stone fell = 16 x + 3 y
∵ The total distance from the top of the cliff to the seabed is
127 meters
∴ The total distance that the stone fell = 127 meters
- Equate the expressions of the total distance
∴ 16 x + 3 y = 127 ⇒ (1)
∵ The time of the stone's entire fall is 12 seconds
∴ x + y = 12 ⇒ (2)
Solve the system of equations to find x and y
Multiply equation (2) by -3 to eliminate y
∵ -3 x - 3 y = -36 ⇒ (3)
- Add equations (1) and (3)
∴ 13 x = 91
- Divide both sides by 13
∴ x = 7 seconds
Substitute the value of x in equation (2) to find y
∵ 7 + y = 12
- Subtract 7 from both sides
∴ y = 5 seconds
The stone fell in the air for 7 seconds and fell in the water for 5 seconds
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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