Stone

$s = 490t - 4.9t^2$

The velocity, v, is found by differentiating the above equation with respect to t.

or, $\frac{ds}{dt}$ = $u$ = 490 - 9.8t

When the stone reaches the highest point, its upward motion stops. Hence, v = 0.

or , -490 = - 9.8 $t$

or, $\dfrac{-490}{-9.8} = t$

or, $t$ = 50

The maximum height can be found by substituting t = 50 seconds into the original equation of motion,

$s = 490$ ( $50$ ) - $4.9$ ( $50^2)$

$s = 24,500$ - ( $4.9 × 2500$ )

$s = 24,500 - 12,250 = 12,250$

Therefore the maximum height reached by the stone thrown upwards is 12250 meters.