Question

The Heigth of a cliff relative to the ocean below is 57 m. Someone kicks a rock horizontally off of the cliff and hears the sound 4.62s later.

a. How long does it take for the rock to hit the water?

b. How far must the sound travel to get back to the cliff? assume that sound moves in a straight line with a speed of 343 m/s.

c. Relative to the base of the cliff, where does the rock hit the water?

d. What was the initial speed given to the rock?

Answer 1

1) The length of time it takes for the rock to hit the water is: (Ref Kinematic equations):
t1 = sqrt(2*d / a) = sqrt (2*57/9.81) = 3.41 sec
Therefore, the length of time it took for the sound to reach your ear is 4.62sec - 3.41sec = 1.21 sec
2.The distance travelled by the sound wave is: d = V * t = 343 * 1.21 = 415.03 m

3) Make a triangle: 57 m is the height, x is the distance from the base of the cliff outward into the water and 394.92 m is the distance from where the rock hit the water back to the cliff (it is the hypotenuse)

Use Pythag. theorem: 57^2 + x^2 = 415.03^2 ----> x = 411.09 m

4) Initial speed of the rock: Vertical Speed = 0, Horizontal speed = horizontal distance / t1 = 411.09 / 3.41= 120.55 m/s

Answer 2

a) The length of time it takes for the rock to hit the water is: (Ref Kinematic equations):
t1 = sqrt(2*d / a) = sqrt (2*57/9.81) = 3.41 sec
Therefore, the length of time it took for the sound to reach your ear is 4.62sec - 3.41sec = 1.21 sec

b)
The distance travelled by the sound wave is: d = V * t = 343 * 1.21 = 415.03 m

c)

Make a triangle: 57 m is the height, x is the distance from the base of the cliff outward into the water and 415.03 m is the distance from where the rock hit the water back to the cliff (it is the hypotenuse)

Use Pythag. theorem: 57^2 + x^2 = 415.03^2 ----> x = 411.1 m

d)

Initial speed of the rock: Vertical Speed = 0 Horizontal speed = horizontal distance / t1 = 411.1 / 3.41 = 120.56 m/s