Problem3 The radius of the earth is approximately R 6400 km. A ball is dropped f

Question

Problem3 The radius of the earth is approximately R 6400 km. A ball is dropped from rest R above the surface of the earth (2R from the center). How fast does it hit the earth? (If one doesn't want to ignore the air, one could ask, how fast it's going when it burns up in the atmosphere. The answer is essentially the same.) The earth's gravity accelerates the ball downward, R2 a=g-2 where g 9.8 or 10m/s2, and y is the distance from the center of the earth. Don't solve the problem. Instead, tell what's fundamentally wrong with this solution: a g(R2)/(2R)2 g/4. The distance traveled is R. u-2aR-2gR/4 9.8 m/s2 x 6.4 x 106 m/2 31.4 x 106m?/s2 The result is v 5.6 km/s. Again, what is wrong with this solution?

Explanation / Answer

Above solution is wrong because we are using equation

V^2 = U^2 + 2*a*S

Above equation is true only when acceleration is constant during motion.

But in this case acceleration is not constant as it's changing w.r.t distance from the center of the earth.

for e.g. at the initial point acceleration is = a = g*(R^2/(2R)^2) = g/4

at a height 3R/2 from center of earth, acceleration will be

a = g*(R^2/(3R/2)^2) = 4g/9

At the height R, acceleration will be = g

So since in this motion acceleration is not constant we can not use this equation to solve.

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