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Answer on Mechanics | Relativity Question for Tim Ferid

Question #4344
A ball is thrown vertically upwards and travels freely under gravity. Three seconds later it has a speed of 4.4 ms-1 but its direction has changed. Find the initial velocity of the particle, can I see working as well?
Expert's answer
<img src="data:image/png;base64,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" alt="">
h0=v0t-gt0^2/2
h1=h0+gt1^2/2
t0+t1=3
v1=sqrt(2gh1)
t1=sqrt(2h1/g)

h0=v0*(3-t1)-g*(3-t1)^2/2
h1=v0*(3-t1)-g*(3-t1)^2/2+gt1^2/2
t0=3-t1
h1=v1^2/2g
t1=sqrt(2v1^2/2g^2)

v1^2/2g=v0*(3-t1)-g*(3-t1)^2/2+gt1^2/2
t1=v1/g

t1=0.45

v0=12.02 m/s

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