Question

A ball is projected upwards from the top of a tower with a velocity $25m{s}^{-1}$ making an angle ${30}^{\circ }$ with the horizontal. The height of tower is $70m$. After how many seconds from the instant of throwing, will the ball reach the ground. ($g=10m{s}^{-2}$)

• A. $2s$
• B. $5s$
• C. $7s$
• D. $9s$

Answer 1

The correct option is C $7s$

Taking upward direction as positive.
since, $y=u_{y}t+\frac{1}{2}{a}_y{t}^2$

or $-70=\left(50\sin {30}^{\circ }\right)t+\left(0.5\right)(-10)t^2$
or $-70=25t-5t^2$
or $t^2-5t-14=0$
or $t^2-7t+2t-14=0$
or $t(t-7)+2(t-7)=0$
or $(t-7)(t+2)=0$
$t=7s$ (negative time invalid)