Question

A stone is thrown vertically upwards with a velocity of 29.4 m/s from the top of a tower 34.3 m high. Find the total time taken by stone to reach the foot of the tower.​

Answer 1

Okay so the journey of the stone can be divided into two parts - the path upwards and the path downwards towards the foot of the building.

For the first part:

u (initial velocity) = 34.3 m/s, and v (final velocity) = 0 (since the stone eventually comes to rest at a point above after which it begins to fall down)

Therefore, 0^2 = 34.3^2 - 2 * 9.8 * S (using v^2 = u^2 + 2gS)

=> S = 60.025 m

And so, time for the first part = (0 - 34.3)/-9.8 = 3.5 s.

For the second part:

u = 0 (starts from rest), v = ?? (unknown), and S = 147 + 60.025 = 207.025 m

and a = g.

Therefore, v^2 = 0^2 + 2 * 9.8 * 207.025 = 4057.69

=> v = 63.7 m/s

=> Time for the second part = (63.7 - 0)/9.8 = 6.5 s.

And so, total time = 6.5 + 3.5 = 10 s

Answer 2

$\sf\huge\underline\purple{question-}$

A stone is thrown vertically upwards with a velocity of 29.4 m/s from the top of a tower 34.3 m high. Find the total time taken by stone to reach the foot of the tower.

$\sf\huge\underline\purple{solution-}$

Okay so the journey of the stone can be divided into two parts - the path upwards and the path downwards towards the foot of the building.

oll

For the first part:

u (initial velocity) = 34.3 m/s, and v (final velocity) = 0 (since the stone eventually comes to rest at a point above after which it begins to fall down)

Therefore,

0^2 = 34.3^2 - 2 * 9.8 * S (using v^2 = u^2 + 2gS)

=> S = 60.025 m

And so, time for the first part = (0 - 34.3)/-9.8 = 3.5 s.

For the second part:

u = 0 (starts from rest), v = ?? (unknown), and S = 147 + 60.025 = 207.025 m

and a = g.

Therefore, v^2 = 0^2 + 2 * 9.8 * 207.025 = 4057.69

=> v = 63.7 m/s

=> Time for the second part = (63.7 - 0)/9.8 = 6.5 s.

And so, total time = 6.5 + 3.5 = 10 s.