7. An astronaut shipwrecked on a distant planet with unknown characteristics is

Question

7. An astronaut shipwrecked on a distant planet with unknown characteristics is on top of a cliff, which he wishes to descend He does not know the acceleration due to gravity on the planet. and he has only a good watch with which to make measurements. He wants to learn the height of the cliff, and to do this, he makes two measurements (Fig. 2-2 ). First, he lets a rock fall from rest off the cliff edge; he finds that the rock takes 4.15 s to reach the distant ground. Second, he releases the rock from the same spot but tosses it upward so that it rises a height of what he estimates to be 2 m before it falls to the ground below. This time the rock takes 6.30 s to reach the ground. What is the height of the cliff? A FIGURE 2-2 Problem 7 15 m-tall huilding. What

Explanation / Answer

7. given time taken to rock to drop off the cliff, t1 = 4.15 s

now, when the rock is given initial upward velocity, t2 = 6.3 s

h2 = 2 m

height of cliff = H

then

-H = 0.5*g*t1^2

g = -H/8.61125

-2*g*h2 = u^2

u = sqrt*(2.1528125*H)

and

-H = u*t2 - 0.5gt2^2

-H = sqrt*(2.1528125*H)*t2 + 0.5*(H/8.61125)*t2^2

H = 7.824 M

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