The maximum height is reached in 5 seconds by a stone thrown vert… - Vidyadip

MCQ

The maximum height is reached in $5$ seconds by a stone thrown vertically upwards and moving under the equation $10s = 10ut -49{t^2}$, where $ s$ is in metre and $t$ is in second. The value of $u$ is ........ $m/\sec $

A
$4.9$
✓
$49$
C
$98$
D
None of these

✓

Answer

Correct option: B.

$49$

b
(b) Given equation is $\frac{{dy}}{{dt}} = - \frac{{16}}{6} = - \frac{8}{3}cm/\sec .$ or $s = ut - 4.9{t^2}$

==> $\frac{{ds}}{{dt}} = u - 9.8t = v$

When stone reached the maximum height, then $v = 0$

==> $u - 9.8t = 0 \Rightarrow u = 9.8\,t$

But time $t = 5\,sec$

So the value of $u = 9.8 \times 5 = 49.0\,m/sec$

Hence initial velocity $ = 49\,m/sec.$

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