Question

A pebble is thrown vertically downwards with a velocity of 5 m/s, and impacts the ground at 10 m/s. If the pebble was thrown vertically upwards from the same height with the same initial sped, with what velocity would it impact the ground after falling back down?

Answer #1

Use equations of kinematics to find the height from which pebble was thrown

v^{2} - u^{2} = 2ah

10^{2} - 5^{2} = 2*9.8*h

100 - 25 = 19.6*h

h = 3.8265 m

Now, if it is thrown vertically upward with initial velocity as 5 m/s, the maximum height gained will be

v^{2} - u^{2} = 2ah

0 - 5^{2} = 2(-9.8)h

h = 25 / 19.6

h = 1.2755 m

Therefore , pebble has to fall a total height of 1.2755 + 3.8265 = 5.1020 m to get back to ground

Now, at the top of its height, the velocity is zero,

so, v^{2} - u^{2} = 2ah

v^{2} = 2*9.8*5.1020

v = 9.99 m/s

v = 10 m/s (approx after rounding off)

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