A ball is thrown vertically upward with an initial velocity of 150 m s - 1 . The ratio of velocity after 3 s and 5 s is x + 1 x . The value of x is _____. {take, g = 10 m s - 2 }

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TestHub · Accepted Answer

The formula to calculate the velocity of the ball after $3 s$ is given by

$v_{3} = u - 3 g . . . (1)$

The formula to calculate the velocity of the ball after $5 s$ is given by

$v_{5} = u - 5 g . . . (2)$

Divide equation (1) by equation (2) to obtain the required ratio.

$\frac{v_{3}}{v_{5}} = \frac{u - 3 g}{u - 5 g} . . . (3)$

Substitute the values of the known parameters into equation (3) to calculate the required ratio.

$\begin{array}{rcl} \frac{v_{3}}{v_{5}} & = & \frac{150 - 30}{150 - 50} \\ = & \frac{120}{100} \\ = & \frac{6}{5} \\ = & \frac{5 + 1}{5} \end{array}$

Comparing the above equation with the given expression, it can be written that $x = 5$ .

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