Question

A stone thrown upwards, has its equation of motion $s=490 t-4.9 t^{2} .$ Then the maximum height reached by it, is

• A. 24500
• B. 12500
• C. 12250
• D. 25400

Answer 1

Answer: (C)

Given that
$s=490 \,t-4.9\, t^{2}$
On differentiating w.r.t. $t$, we get
$\frac{d s}{d t}=490-9.8 t$
A stone is reached the maximum height,
when $\frac{d s}{d t}=0$
$\Rightarrow 490-9.8 t=0$
$\Rightarrow t=\frac{490}{9.8}$
$=\frac{100}{2}=50$
$\therefore $ Maximum height at $t=50$
$s =490(50)-4.9(50)^{2}$
$=24500-12250$
$=12250$