Question

A body is thrown vertically upwards and rises to a height of 10 m. The time taken by the body to reach the highest point is :

• A. 1.43 s
• B. 4.1 s
• C. 1.24 s
• D. 2.86 s

Answer 1

The correct option is A 1.43 s

Using 1st equation of motion,

$v=u+at$

Final velocity of the body is zero, i.e. $v=0$

Acceleration $a=-g=-9.8m/s^2$

So, $0=u-gt$

$\Rightarrow u=gt...\left(i\right)$

Now let us consider 2nd equation of motion,

$s=ut+\frac{1}{2}a{t}^2$

Height reached $=10m$

Using (i), we get

$\Rightarrow 10=\left(gt\right)t-\frac{1}{2}g{t}^2$

$\Rightarrow 10=\frac{1}{2}g{t}^2$

$\Rightarrow t=\sqrt{\frac{10\times 2}{g}}$

$\Rightarrow t=\sqrt{\frac{10\times 2}{9.8}}$

$\Rightarrow t=\sqrt{2.0408}$

$\Rightarrow t=1.428\approx 1.43sec$