## 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 spe

Question

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.

in progress 0
3 days 2021-10-12T11:55:42+00:00 2 Answers 0

7 secs air and 5 secs in water

Step-by-step explanation:

2. 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