Solving for Cliff Height: An Alert Hiker's Task

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In summary, An alert hiker observes a boulder falling from the top of a distant cliff and notes that it takes 1.3s for the boulder to fall the last 3rd of the way to the ground. The height of the cliff can be determined by using the equation y = yo + vit + 0.5gt^2 and solving for y. If there are two solutions, the extraneous one represents a physically impossible scenario.
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black_hole
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Homework Statement



An alert hiker sees a boulder fall from the top of a distant cliff and notes that it takes 1.3s for the boulder to fall the last 3rd of the way to the ground. Ignore air resistance.a) what is the height of the cliff in meters? b) If in part a) you get 2 solutions what does the extraneous one represent?

Homework Equations





The Attempt at a Solution



looking at the last 3rd
Vi = ?
Vf = 0 m/s
a = -9.8 m/s/s
t = 1.3s
x = ?

possibly going to use this equation: x = xo +vit +.5at^2 ?
 
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  • #2
you should use the equation y = yo +vit +.5gt^2 for vertical motion.
also Vi should equal zero, as the boulder begins from rest in the y-axis and Vf should equal the final velocity as the boulder hits the ground
 

FAQ: Solving for Cliff Height: An Alert Hiker's Task

1. How do you determine the height of a cliff?

To determine the height of a cliff, you can use the equation h = vt2/2, where h is the height, v is the initial velocity, and t is the time it takes for an object to fall from the top of the cliff to the ground. You will need to measure or estimate the initial velocity and time accurately to get an accurate result.

2. What tools do I need to solve for cliff height?

To solve for cliff height, you will need a stopwatch or timer to measure the time it takes for an object to fall, and a measuring tape or ruler to measure the distance the object falls from the top of the cliff to the ground. You may also need a calculator to perform the necessary calculations.

3. Can I use any object to solve for cliff height?

Yes, you can use any object that you can drop from the top of the cliff and measure the time it takes to fall and the distance it falls. However, it is important to use a relatively small and dense object to minimize the effects of air resistance on the object's fall.

4. What are some common mistakes when solving for cliff height?

Some common mistakes when solving for cliff height include not accurately measuring the distance or initial velocity, not starting the timer at the right time, and not accounting for the effects of air resistance. It is important to carefully measure and record all necessary variables to get an accurate result.

5. Can this method be used to solve for the height of any object?

This method can only be used to solve for the height of an object that is dropped from a known height and falls freely under the influence of gravity. It cannot be used for objects that are launched or thrown horizontally, or for objects that are affected by other forces such as air resistance or friction.

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