Answer to Question #152732 in Classical Mechanics for GuardianVex

Question

A ball is thrown vertically upwards with a velocity of 20 m/s from the top of the building of height 25m from the ground (i).How high will the ball reach? (ii)How long will it take to reach the A ground?

Answer 1

As per the given question,

Initial speed of the ball (u)=20 m/s

Height of the building (h)= 25m

At the top most point the speed of the ball become zero hence,

Let the height reached by the ball from the top of the building be H and gravitational acceleration be $g=10 m/s^2$ .

applying newton's third equation of motion,

$v^2=u^2-2gH$

Now, substituting the values,

$\Rightarrow 0=20^2-2\times g\times H$

$\Rightarrow H = \frac{400}{2\times 10}=20 m$

Hence, total height from the ground be $=H+h = 25+20=45m$

Let the time taken by the ball to reach the ground be t.

$-h=ut-\frac{gt^2}{2}$

$\Rightarrow -25=20t -5t^2$

$\Rightarrow 5t^2-20t-25=0$

$\Rightarrow t^2-4t-5=0$

$\Rightarrow t^2-5t+t-5=0$

$\Rightarrow t(t-5)+1(t-5)=0$

$(t-5)(t+1)=0$

Hence time taken by the ball to reach the ground be 5 second.