A ball is projected upwards from the top of tower with a velocity $50\,\,m{s^{ - 1}}$ making an angle ${30^o}$ with the horizontal. The height of tower is $ 70 \,m$. After how many seconds from the instant of throwing will the ball reach the ground ........ $\sec$
A ball is projected upwards from the top of tower with a velocity $50\,\,m{s^{ - 1}}$ making an angle ${30^o}$ with the horizontal. The height of tower is $ 70 \,m$. After how many seconds from the instant of throwing will the ball reach the ground ........ $\sec$
$2$
$5$
$7$
$9$
A ball is projected upwards from the top of tower with a velocity $50\,\,m{s^{ - 1}}$ making an angle ${30^o}$ with the horizontal. The height of tower is $ 70 \,m$. After how many seconds from the instant of throwing will the ball reach the ground ........ $\sec$
The vertical component of velocity of projection $ = - 50\sin 30^\circ = - 25\,m/s$
If $t$ be the time taken to reach the ground,
$h = ut + \frac{1}{2}g{t^2}$
$⇒$ $70 = - 25t + \frac{1}{2} \times 10{t^2}$
$⇒$ $70 = - 25t + 5{t^2}$
$⇒$ ${t^2} - 5t - 14 = 0$
$⇒$ $t= -2s$ and $7s$
Since, $t = -2s$ is not valid
$\therefore t = 7\, s$
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