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How much time elapses from when the rock is thrown until it hits the street? express your answer with the appropriate units.

User Eol
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1 Answer

3 votes

Final answer:

To determine how long it takes a rock to fall 30.0 meters, we use the equation of motion s = ut + 1/2 at^2. With initial velocity u being zero and 'a' as the acceleration due to gravity, we find the time 't' to be apaproximately 2.47 seconds.

Step-by-step explanation:

To calculate the time it takes for a rock to hit the ground from a certain height, one can use the kinematic equations of motion under the influence of gravity. The key equation we will use is:

s = ut + 1/2 at^2

Where:

  • s is the displacement (height from which the rock is dropped)
  • u is the initial velocity (0 m/s if the rock is simply dropped)
  • a is the acceleration due to gravity (9.8 m/s^2 on Earth)
  • t is the time in seconds

For a rock dropped from a height of 30.0 meters, the equation considering u = 0 becomes:

30.0 = 0 * t + 1/2 * 9.8 * t^2

Solving this quadratic equation for t, we get:

t^2 = (2 * 30.0) / 9.8

t^2 = 6.12244897959

t = sqrt(6.12244897959)

t ≈ 2.47 seconds

So, the rock takes approximately 2.47 seconds to hit the ground.

User Billy Boyo
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7.6k points
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