Question

A stone is thrown up vertically and the height $'x'$ ft reached by it in time $'t'$ secs is given by $x = 80t - 16t^2$ . The stone reaches the maximum height in time ?

• A. $2 \,secs$
• B. $2.5\, secs$
• C. $3\, secs$
• D. $3.5\, secs$

Answer 1

Answer: (B)

$2.5\, secs$

Answer 2

We have , $x = 80 t - 16t^2$
$\therefore \:\:\: \frac{dx}{dt} = 80 - 32 t$
Now , $\frac{dx}{dt} = 0 \Rightarrow 80 - 32 t = 0$
$\Rightarrow \:\: t = \frac{5}{2}$
Now, $\frac{d^2 x}{dt^2} = - 332 \: \Rightarrow \frac{d^2 x}{dt^2}|_{t = \frac{5}{2}} = - 32 < 0$
$\Rightarrow \:\: t = \frac{5}{2}$ is maximum point
Hence, the stone reaches the maximum height in time, $t = \frac{5}{2} = 2.5$ secs