Question

Devise a way to determine the height of a building using ONLY a stopwatch. Please expound.

thank you

Answer 1

In the above question we have to find distance using time.

For this we may assume that the stone has to be thrown from the top of the building whose height has to be found, in a straight/linear direction downwards.

For this we have to use second equation of motion,

i . e ,

d = V_°t + 1/2 a t²

where,

V_° = initial velocity of the object

t = time taken by the object (stone) to reach the ground

a = gravitational acceleration = 9.81 m/s²

In this equation V_° which is initial velocity will always be zero as the stone is dropped from the rest.

To get a clear view let's take an example where a stone has been thrown from a top of the building , and it took 20 seconds to reach the ground.

So here,

Time = 20 sec.

Gravity = a = g = 9.81m/sec²

Initial velocity = V_° = 0 m/sec Height of building = d = h = ?

Now by using 2nd equation of motion.

d = V_°t + 1/2 a t²

d = (0 x 20)+1/2 x (9.81 x 20²)

d = 1962 meters

Therefore, we obtain a equation for determining the height using stopwatch as,

h = 1/2 at²