Height testing

Classical Mechanics Level 2

A boy drops a stone from the edge of a cliff such that it plops into a lake to test the height of the cliff. If he heard the sound after 3 seconds of him dropping the stone, how high is the cliff?

Note: here the speed of sound is 300m/s.

Take g=10 m / s 2 m/s^2

Put your answer in metres.*


The answer is 41.

Krishna Karthik by Krishna Karthik , 15, Australia

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1 solution

Gabriel Chacón
Dec 4, 2018

Here is a different method that avoids the second-degree equation. (It doesn't pay much in this case, but it can be very useful when the resulting equation is not easy to solve):

  • Estimate the height neglecting the time the sound needs to travel up: h = 1 2 10 ⋅ 3 2 = 45 m h=\frac{1}{2}10\cdot3^2=45 \text{ m}

  • Use this height to estimate the time the sound needs to travel up: t s o u n d = 45 300 = 0.15 s t_{sound}=\frac{45}{300}=0.15 \text{ s}

  • Correct the fall time and calculate the height again: h = 1 2 10 ⋅ 2.8 5 2 = 40.6 m ≈ 41 m h=\frac{1}{2}10\cdot2.85^2=40.6 \text{ m}\approx 41 \text{ m}

  • Repeat these steps to gain precision if you wish.

What is the condition for this method to work efficiently in this case?

2 Helpful 1 Interesting 1 Brilliant 0 Confused

Good solution. I think it does avoid some of the difficulties of a second degree equation.

Krishna Karthik - 2 years, 6 months ago

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