Question

An object is thrown up with velocity 30 m/s from top of 100 m tall tower. Calculate the time required for the object to reach the ground.

Answer 1

buddy , there is an error ... Total distance to reach ground is 45+100 = 145 m

Here is your answer buddy... hope this helps you

Answer 2

We know that:

Ball is thrown upwards.

Given:

Initial velocity = 30 m/s

Final velocity = 0

Acceleration (a):

$\implies$ -g

$\implies$ -10 m/s²

Note: Since, the ball is thrown against the gravity.

Now:

$\huge\boxed{\sf{v^{2}- u^{2}= 2\:aS}}$

$\implies$ (0)² - (30)² = 2aS

$\implies$ 0 - 900 = 2aS

$\implies$ 0 - 900 = 2(-10)S

$\implies$ 0 - 900 = - 20S

$\implies$ S = 45 m

And:

Height to which the ball reaches from the top of the tower is 45 m.

Therefore:

Height to which the ball reaches from the surface of the earth:

$\implies$ (100 + 45) m

$\implies$ 145 m

Now:

Time taken by the ball to reach the height of 45 m from the top of the tower is given by the formula:

$\huge\boxed{\sf{v - u = at}}$

So:

$\implies$ 0 - 30 = (-10)(t)

$\implies$ t = 3 seconds

We know:

$\boxed{\sf{Time\:of\:Ascent = Time\:of\:Descent}}$

Therefore:

Time taken by the ball to again reach the top of the tower: 3 seconds

When the ball starts falling from the height of 145 m.

Now:

At the Height of 145 m:

Initial velocity of the ball = 0 

Final velocity = v

Time taken to reach the top of tower = 1 sec

And:

Acceleration due to gravity = 10 m/s²

Firstly:

We will find the final velocity of the ball, after which we can calculate the total time.

Therefore:

Height = 105 m

Note: From the top of the tower is taken.

$\huge\boxed{\sf{v^{2} - u^{2}=2\:ah}}$

$\implies$ v² - (0)² = 2(10)(105)

$\implies$ v² = 2100

$\implies$ v = 45.82 m/s

Hence: The velocity by which the ball is falling is 45.82 m/s.

Now:

For Finding the total time:

Height of the ball (H) = 145 m

Initial Velocity of the ball (u) = 0 m/s

Note: Since the ball is under the free fall.

Final Velocity of the ball (v) = 30 m/s

Acceleration = 10 m/s²

Now:

Using the Formula:

$\huge\boxed{\sf{S = ut + \frac{1}{2} at^{2}}}$

$\implies$ 145 = (0)(t) + 1/2 × 10 (t)²

$\implies$ t² = 145/5

$\implies$ t² = 29

$\implies$ t = 5.38 sec

Hence:

Total time taken:

$\implies$ 3 + 5.38

$\implies$ 8.38 sec