A ball is thrown upwards from the ground with an initial speed of u. The ball is at a height of 80 m at two times, the time interval being 6 s. Find u. Take $g=10m/s^2.$

Here, $u=um/s,a=g=-10m/s^{2}ands=80m$

Substituting the values in $s=ut+\frac{1}{2}a{t}^2,$ we have $80=ut-5t^2$

$5t^2-ut+80=0$

$t=\frac{u+\sqrt{u^2-1600}}{10}and\frac{u-\sqrt{u^2-1600}}{10}$

Now, it is given that $\frac{u+\sqrt{u^2-1600}}{10}-\frac{u-\sqrt{u^2-1600}}{10}=6$

$\frac{\sqrt{u^2-1600}}{10}=6or\sqrt{u^2-1600}=30$

$u^2-1600=900$

$\therefore u^2=2500$

$u=\pm 50m/s$

Ignoring the negative sign, we have $u=50m/s$