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Q.
A stone is thrown horizontally with velocity $u$. The velocity of the stone 0.5 s later is $3 u / 2$. The value of $u$ is
Motion in a Plane
Solution:
At $t=0.5\, s$,
the vertical component of velocity is
$v_{t}=g t=g(0.5)=\frac{g}{2}=4.9 \,m / s$
Hence at $t=0.5 s ,$ we have
$\sqrt{v_{t}^{2}+u^{2}}=\frac{3 u}{2} $ or $(4.9)^{2}+u^{2}=\frac{9 u^{2}}{4}$
or $ 5 u^{2}=4 \times(4.9)^{2}$ or $u^{2}=(0.8)(4.9)^{2}$
or $ u=(4.9) \sqrt{0.8}=4.4 \,m / s$