A stone is dropped from the top of a cliff. The splash it makes when striking...

A stone is dropped from the top of a cliff. The splash it makes when striking the water below is heard 2.5 s later. The speed of sound in air is 343 m/s. How high is the cliff?

Expert Solution

Solution:

Let t₁ be the time taken by the rock to touch the water and.

t₂ be the time taken by the sound to reach us.

Given that t₁ + t₂ = 2.5 s    -------------(1)

Velocity of sound v = 343 m/s

Let S be the distance taveled by the rock.
          t₂ = S/v = S/343 ........... (2)
from eq. of motion, S = (1/2)g(t₁)² (initial speed u =0)
         t₂ = [(1/2)(9.8 m/s²)(t₁)²]/(343 m/s) = 0.014286(t₁)² ..........(3)
substitute the eq (3) in eq (1), we get
     0.014286(t₁)² + t₁ - 2.5 = 0
On solving the above quadratic equation we get
                      t₁ = 2.416 s

Hence distance covered by the rock is

S = (1/2)(9.8 m/s²)(2.416 s)²

S = 28.63 m

genius_generous answered 2 years ago

A stone is dropped into a well. The sound of the splash is heard 2.92 s...

A stone is dropped into a well. The sound of the splash is heard 2.92 s later. What is the depth of the well? (Take the speed of sound to be 343 m/s.)

A stone is dropped into a well. The splash is heard 2.2 seconds later. What is...

A stone is dropped into a well. The splash is heard 2.2 seconds later. What is the depth of the well to the nearest tenth of a meter?

2) A ball is dropped from rest at the top of a high cliff. It takes...

2) A ball is dropped from rest at the top of a high cliff. It takes 10.00 seconds for the ball to reach the ground below. Find: a) the height of the cliff, b) the velocity of the ball hitting the ground below, c) the time it takes for the ball to fall half of the cliff's height, and d) the velocity at this halfway point. (Remember acceleration due to gravity is -9.800 m/s^2).

Two stones are dropped from the edge of a 60-m cliff, the second stone 2.0 s...

Two stones are dropped from the edge of a 60-m cliff, the second stone 2.0 s after the first. How far below the top of the cliff is the second stone when the separation between the two stones is 40 m?

A stone is dropped inside a well. The sound produced when the stone hits the bottom...

A stone is dropped inside a well. The sound produced when the stone hits the bottom of the well is heard 4.3 s later. How deep is the well, in meters? The speed of sound is 338 m/s

A stone is dropped from the roof of a building, 1.10s after that a second stone...

A stone is dropped from the roof of a building, 1.10s after that a second stone is thrown straight down with an initial speed of 20.0 m/s & the two stones land at the same time How high is the building h=???m

A stone is dropped from a bridge. A second stone is thrown downwards 2.0 s later...

A stone is dropped from a bridge. A second stone is thrown downwards 2.0 s later with an initial speed of 25 m/s. They both reach the water below at the same instant. (a) How long did it take for the first stone to reach the water? (b) How high is the bridge? (c) What are the speeds of the two stones just before they hit the water?

A stone is dropped into a river from a bridge at a height h above the...

A stone is dropped into a river from a bridge at a height h above the water. Another stone is thrown vertically down at a time t after the first is dropped. Both stones strike the water at the same time. What is the initial speed of the second stone? Give your answer in terms of the given variables and g.

A stone is dropped at t = 0. A second stone, with twice the mass of...

A stone is dropped at t = 0. A second stone, with twice the mass of the first, is dropped from the same point at t = 234 ms. How far below the release point is the center of mass of the two stones at t = 326 ms? (Neither stone has yet reached the ground.) Tries 0/10 How fast is the center of mass of the two-stone system moving at that time?

A cannonball is fired horizontally from the top of a cliff. The cannon is at height...

A cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 100m above ground level, and the ball is fired with initial horizontal speed v0=0. Assume acceleration due to gravity to be g = 9.80 m/s2. a)Assume that the cannon is fired at time t=0 and that the cannonball hits the ground at time tg. What is the y position of the cannonball at the time tg/2? b) Given that the projectile lands...

Question