A falling ball

Classical Mechanics Level 1

A ball dropped from the roof of a building with zero initial speed takes 2 seconds to reach the ground. There is a small window exactly at the middle of the building. How much time does the ball take to reach the window?

Details and Assumptions:

Air drag is neglected.
Acceleration due to gravity during the fall is constant.

Less than 1 second 1 second More than 1 second

7 solutions

Rohit Gupta
Mar 23, 2017

When a particle is dropped, it is accelerated by the gravity continuously in the downward direction. Therefore, in the first half of the fall, its speed is lesser than in the second half. This implies it will take greater time in the first half than the second half.

The total time of the fall is 2 seconds. The time taken in the first half of the fall should be greater than 1 second and that in the second half is less than 1 second. So that the total time taken is still 2 seconds.

Why if the ball suffers some air resistance

Biswajit Barik - 4 years ago

Even if the ball suffers air resistance still the time taken in the second half will be less than the first half. Because even after the air resistance the speed of the particle will increase as it falls and even if it reaches the terminal velocity, it will obviously be more than the initial speed that was zero.

Rohit Gupta - 4 years ago

good explaination thanks

Biswajit Barik - 4 years ago

Soorya Saravanan
Mar 12, 2017

The initial velocity of the particle is zero. After traveling half the distance it would have attained some velocity. But acceleration is same in both the cases. So the second half of the distance will be traveled faster by the object than the first half. So the time taken by the object is more during the first half.

Yes, as the speed is increasing with the fall, the second half will be traveled in lesser time.

Rohit Gupta - 4 years, 3 months ago

A Former Brilliant Member
Apr 17, 2017

By Galileo's law for freely falling objects they traverse odd unit of distance in equal interval of time starting with unity. 1st sec 1 unit. (Totally 1unit) 2nd sec 3 unit .... (Totally 4units) Thus in 2 sec follow 4 units. Hence for 2 units takes more than 1 sec. Approx 4/3 sec

Ramiel To-ong
May 23, 2017

Using Projectile formula: H = 0.5(G)(2)^2 = 19.62-----------Height of the building if H = H/2 The time t-------------- 19.62/2 = 0.5(G)(t)^2 t = 1.414 more than one second>>>>>>>>>>>>

Robert DeLisle
May 14, 2017

d = vt + at^2. v=0. a = 10 (rounded a bit).

Height = 40 (distance traveled in 2 seconds).

Distance traveled in 1 sec = 10.

Halfway = 20. More than one second.

Aarsh Verdhan
Mar 11, 2017

From kinematics height of building is equal to 20 m so height of window 10m hence time is sqrt(2) sec which is >1 g is 10ms^2 (assumed)

Can you further elaborate how you reached the result that the height of the building is $20 \text{m}$ ? Which equations you are using to do the calculations.

Moreover, do we really need to solve for these values or can we say it directly from the logic that the time taken to cover first half will be more than 1 second?

Rohit Gupta - 4 years, 3 months ago

Though we can use the logic but getting on with the equations gives you an upper hand in exams.

From $s=ut+1/2gt^2$ (where u=0) S=2g

Now applying the same eq keeping s=g you will get $t=\sqrt {2} >1$ .

Aarsh Verdhan - 4 years, 3 months ago

"logic" when simple equations are at hand is often dismissed as "hand waving" where I went to school.

Robert DeLisle - 4 years ago

James Evans
Mar 10, 2017

Using Suvat equations, distance to the bottom is 2g (g=9.8m/s^2). Time to a distance of g metres is t=\sqrt {2}s>1s.

Oh, can you further elaborate on how you got the distance to the bottom? Especially, what are "Suvat" equations?

Rohit Gupta - 4 years, 3 months ago

https://www.google.co.in/search?q=Suvat+equations&oq=Suvat+equations&aqs=chrome..69i57&sourceid=chrome&ie=UTF-8

A Former Brilliant Member - 4 years, 2 months ago

A falling ball

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