A rock is thrown straight down from a cliff with an initial velocity of 10.0 m/s. Its final velocity when it strikes the water below is 115 m/s. How long is the rock in flight?

Respuesta :

The time of the rock in flight is 10.71 s.

What is time of flight?

This is the total time taken for an object or a projectile to return back to the same plane at which it was projected.

To calculate the time of the rock in flight, we use the formula below.

Formula:

  • v = u+gt............. Equation 1

Where:

  • v = Final final velocity
  • u = Initial velocity
  • t = time of the rock in flight.
  • g = acceleration due to gravity

make t the subject of the equation

t = (v-u)/g.................... Equation 2

From the question,

Given:

  • u = 10 m/s
  • v = 115 m/s
  • g = 9.8 m/s².

Substitute these values into equation 2

  • t = (115-10)/9.8
  • t = 105/9.8
  • t = 10.71 s

Hence, the time of the rock in flight is 10.71 s.

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The rock was in the flight for 11.7 s

Time of flight

This is defined as the total time spent by an object in air.

Determination of the height of the cliff

From the question given above, the following data were obtained:

  • Initial velocity (u) = 10 m/s
  • Final velocity (v) = 115 m/s
  • Acceleration due to gravity (g) = 9.8 m/s²
  • Height of cliff (h) =?

v² = u² + 2gh

115² = 10² + (2 × 9.8 × h)

13225 = 100 + 19.6h

Collect like terms

13225 – 100 = 19.6h

13125 = 19.6h

Divide both side by 19.6

h = 13125 / 19.6

h = 669.64 m

How to determine the time of flight

  • Acceleration due to gravity (g) = 9.8 m/s²
  • Height of cliff (h) = 669.64 m
  • Time of flight (t) =?

h = ½gt²

669.64 = ½ × 9.8 × t²

669.64 = 4.9 × t²

Divide both side by 4.9

t² = 669.64 / 4.9

Take the square root of both side

t = √(669.64 / 4.9)

t = 11.7 s

Thus, the rock was in the flight for 11.7 s

Learn more about motion under gravity:

https://brainly.com/question/20385439

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