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1D Kinematics

If train A leaves from El Paso at high noon and train B leaves from Dallas at 1 PM, you won't know when they meet unless you master 1D kinematics. What are you waiting for?

Level 1-2

         

It takes about eight and a half minutes for light to reach the earth from the sun. How far away is the sun (in meters)?

Details and assumptions:

  • The speed of light in vacuum is \(3 \times 10^8~\mbox{m/s}\).

Tim's father has a very large farm that spans several kilometers. During a heavy thunderstorm, he is worried that lightning could have destroyed his barn that is located 1,700 meters from the house. He constantly stares out the window, and feels completely helpless.

If lightning did indeed strike the barn, how long (in seconds) does it take between Tim seeing the lightning strike and hearing the sound of thunder?

Note: Light travels at 300,000,000 m/s, and sound travels at 340 m/s.

Image credit: Wikipedia Jakez

A Ball thrown upwards from the top of a building takes 9 seconds to reach to the ground. The same ball when thrown in downwards direction with the same initial velocity takes 4 seconds to reach to the bottom. How much time will the ball take to reach the ground if it is dropped from the top of the same building?

A body travels half of its total path in the last second of its free fall (starting from rest). What is the total duration of the fall of the body in seconds?

Suppose your friend lives in Sydney, Australia, and today the Indian Prime minister, Narendra Modi, is about to deliver a speech in the Opera House. Your friend has reserved a seat 20 meters from the microphone. You are listening to the same speech on the radio in Mumbai, roughly 10,000 km from Sydney.

Suppose the time it takes the sound to reach you is \(t_\textrm{radio}\) and the time is takes to reach your friend is \(t_\textrm{live}\). How much faster the sound reach you, compared to your friend (i.e. find \(t_\textrm{live}/t_\textrm{radio}\))?

Details and Assumptions:

  • Take the speed of sound to be \(300 \text{ m/s}\).
  • The speed of radio waves is \(300,000 \text{ km/s}\).
Image Credit: Youtube Prime Minister Narendra Modi's Full Speech In Sydney, Australia.
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