A ball is thrown vertically downwards from a height of 20 m with a initial velocity v0. It colloids with the ground, loses 50 % of its energy in collision and rebounds to the same height. The initial velocity v0 is .....??? Please explain it briefly.

Answer 1

#v_0 = 19.82 m/s#

v = v0 + g t h = v0 t + g t²/2 = 20 (Everything measured downwards)

#E_k# = (1/2) m v² => #E_p# = m g h = 196.2 m = (1/4) m v² => v ² = 784.8 => v = 28.014 m/s

28.014 = v0 + 9.81 t 20 = v0 t + 4.905 t²

#=># 20 = (28.014 - 9.81 t) t + 4.905 t² = 28.014 t - 4.905 t² #=># 4.905 t² - 28.014 t + 20 = 0 This is a quadratic equation in t t = (28.014 #\pm# 19.809)/9.81 The solution with the - sign yields t = 0.836 s #=># v0 = 19.82 m/s
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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