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(B) Using the first equation of motion,$v = u + at$.Here,initial velocity $u = 150\,m/s$,acceleration $a = -g = -10\,m/s^2$,and $t$ is the time in sec

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$5$

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(B) Using the first equation of motion,$v = u + at$.Here,initial velocity $u = 150\,m/s$,acceleration $a = -g = -10\,m/s^2$,and $t$ is the time in seconds.So,$v(t) = 150 - 10t$.Velocity after $3\,s$ is $v(3) = 150 - 10(3) = 150 - 30 = 120\,m/s$.Velocity after $5\,s$ is $v(5) = 150 - 10(5) = 150 - 50 = 100\,m/s$.The ratio of velocities is $\frac{v(3)}{v(5)} = \frac{120}{100} = \frac{6}{5}$.Given that the ratio is $\frac{x+1}{x}$,we have $\frac{x+1}{x} = \frac{6}{5}$.Comparing the terms,$x = 5$.

$A$ ball is thrown vertically upward with an initial velocity of $150\,m/s$. The ratio of velocity after $3\,s$ and $5\,s$ is $\frac{x+1}{x}$. The value of $x$ is $...........$ Take $g=10\,m/s^2$.

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