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Freefall & Motion

A ball is pro...

Question

A ball is projected vertically upwards crosses a point at a height h after time $3 s e c$ and $5 s e c$ . Initial speed of throw of the ball is $[g = 10 m / s^{2}]$

20 m / s

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40 m / s

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10 m / s

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60 m / s

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Solution

The correct option is B $40 m / s$
If its initial speed is $u$ and the height at time $t$ can be written as $h = u t - g t^{2} / 2 = u t - 5 t^{2}$
or $5 t^{2} - u t + h = 0$
Above equation is a quadratic in $t$ so sum of roots will be $t_{1} + t_{2} = - \frac{- u}{5}$ but sum is given as $3 + 5 = 8 s e c o n d$ so $u = 8 \times 5 = 40 m / s$
Option B is correct.

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A ball is projected vertically upwards crosses a point at a height h after time 3 sec and 5 sec. Initial speed of throw of the ball is [g=10 m/s2]

The correct option is B 40 m/sIf its initial speed is u and the height at time t can be written as h=ut−gt2/2=ut−5t2 or 5t2−ut+h=0Above equation is a quadratic in t so sum of roots will be t1+t2=−−u5 but sum is given as 3+5=8second so u=8×5=40m/sOption B is correct.

A ball is projected vertically upwards crosses a point at a height h after time $3 s e c$ and $5 s e c$ . Initial speed of throw of the ball is $[g = 10 m / s^{2}]$