Question

A stone thrown vertically up from the top of a tower with a velocity of 20m/s reaches the ground in 6s.find the height of the tower

Answer 1

$\huge{\underline{\underline{.........Answer.........}}}$

$\huge{\underline{Given:-}}$

Thrown vertically up with 20 m/s from top of the tower.

It reaches the ground in 6 seconds.

$\huge{\underline{Explanation:-}}$

As the stone is thrown upward it will reach its highest point and at that point its velocity will be zero.

Let it reaches highest point at time "t".

Now,

u = 20 m/s.

v = 0 m/s.

a = - 10 m/s^2.

t = ?.

From first kinematics equation.

$\huge{\boxed{\boxed{v = u + at}}}$

${t = \frac{v - u}{a}}$

Substituting the values.

${t = \frac{0 - 20}{-10}}$

$\huge{\boxed{\boxed{t = 2 seconds}}}$

Now for free fall the time taken is

t' = 6 - 2

t' = 4 seconds.

u = 0 m/s.

a = 10 m/s^2.

S = H(Height of tower)

From second kinematic equation.

$\huge{\boxed{\boxed{S = ut' + \frac{1}{2} a {t'}^{2}}}}$

Substituting the values.

${H = 0 + \frac{1}{2} \times10 \times {4}^{2}}$

${H = 80 meters}$

$\huge{\boxed{\boxed{H = 80 meters}}}$

So,the height of tower is 80 meters