Question

A body is dropped from a top of a tower. If it falls through 40 m during last 2 secs of its fall. What is height of tower?

Answer 1

Answer:

The height of tower is 45 meters

Step-by-step explanation:

Calculation to find the final velocity 'Vf' when body hits the ground:

"First we find the velocity of body when its height is 40 meter"

Let

Velocity of body when its height is 40 meter = Vi

Time taken to fall on the ground form height 40 m = t = 2 sec

Height of body = S = 40 m

Gravitational acceleration = g = 10 m / s²

Calculation:

we know that

According to second equation of motion

            S = Vi × t + (1/2) × g × t²

Putting values we get

           40 = Vi × 2 + (1/2) × 10 × (2)²

⇒          40 = Vi × 2 + 20    

⇒           Vi = 10 m/s

And

we know that

According to first equation of motion

        Vf = Vi + g × t

putting values we get

        Vf = 10 + 10 × 2

⇒      Vf = 30 m/s

NOW

Data:

The final velocity when it hits the ground = Vf = 30 m/s

Initial velocity of body on the top of tower = Vi = 0 m/s

Gravitational acceleration = g = 10 m/s²

Required:

Height of tower = S = ?

Calculation:

We know that

According to third equation of motion

           2 × g × S = (Vf)² - (Vi)²

Putting the values we get

         2 × 10 × S = (30)² - (0)²

⇒            20 × S = 900

⇒                    S = 45 m

So the height of tower is 45 meters

Answer 2

This question can be solved by easiest method.

A body is dropped from a top of a tower.

so, initial velocity of body equals zero. i.e., u = 0

Let height of tower is h and time taken to reach the ground from tower is t.

using formula, S = ut + 1/2at²

here, S =-h , u = 0, a = -g

then, -h = -1/2gt²

or, h = 1/2gt² ........(1)

again, it falls through 40m during last 2 sec of its fall.it means body falls already (h - 40)m distance during (t - 2) sec.

so, using formula, S = uT+ 1/2aT²

here, s = -(h - 40)m , u = 0, a= -g and T = t - 2

so, -(h - 40) = -1/2 g(t - 2)²

or, h - 40 = 1/2 g(t - 2)²

or, h = 40 + 1/2 g(t - 2)²..... (2)

from equations (1) and (2),

1/2 gt² = 40 + 1/2g(t - 2)²

or, 5t² = 40 + 5(t² - 4t + 4)

or, 5t² = 40 + 5t² - 20t + 20

or, t = 3 sec

putting t = 3 in equation (1),

h = 1/2 × 10 × 3² = 45m

hence, answer is 45m.