MATH SOLVE

3 months ago

Q:
# 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 3m/s before hitting the seabed. The total distance from the top of the cliff to the seabed is 127 meters, and the stone's entire fall took 12 seconds.How long did the stone fall in the air and how long did it fall in the water?The stone fell in the air for____ seconds and fell in the water for ____ seconds.

Accepted Solution

A:

The stone fell in the air for 7 seconds and fell in the water for 5 secondsStep-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/sIn the water, it had an average speed 3 m/s before hitting the seabedThe total distance from the top of the cliff to the seabed is 127 metersThe stone's entire fall took 12 secondsWe need to find how long the stone fell in the air and how long it fell in the waterAssume that the time that the stone took to fall in the air is xAssume 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 xAdd 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 yMultiply 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 secondsSubstitute the value of x in equation (2) to find y∵ 7 + y = 12- Subtract 7 from both sides∴ y = 5 secondsThe stone fell in the air for 7 seconds and fell in the water for 5 secondsLearn more:You can learn more about the system of equations in brainly.com/question/2115716#LearnwithBrainly