Mechanics | Relativity Answers

6. A baseball player hits a ball from 1.3 m above the ground with an initial velocity of 36 m/s at an angle of 45. Will it clear a 7.5 m wall located 125 m away?

A cannon fires a shell at 200 m/s at an angle of 65 above the horizontal. a) What is the velocity of the shell after 32 s? Give both the x- and y-components, and then convert it into standard vector form, stating speed and direction. b) How long will it take for the shell to land? c) How far will the shell travel? Assume level ground.

You are standing at an Los Angeles Spaceport observing a spaceship travelling towards you at 0.95 times the speed of light.

The captain of the spaceship, who is stationed midway between the front and rear of the ship, sends out radio signals to turn on light beacons located at the front and rear of the ship. He observes both beacons to be turned on simultaneously.

Without performing any calculations, describe and explain in your own words what is observed by you on the ground in Los Angeles. Use diagrams to illustrate your answer.

Before it leaves Earth you observe the length of another spacecraft to be 200 m. After take-off, the craft travels past Earth (to wave good bye!) while moving at a velocity of 95% of the speed of light. You are assigned the task of re-measuring its length as it travels past.

a) Explain, at a fundamental level (i.e. with the principles of relativity in mind), how must you perform this measurement?

b) What value will you obtain? (ANS: 62m)

During machine testing time, a proton in the Large Hadron Collider travels at 0.999990 c, where
c is the velocity of light.

a) Find the total energy of the proton. (ANS: 3.36144 x 10-8 J or 0.209804 TeV)
b) Find its kinetic energy. (ANS: 3.34641 x 10-8 J or 0.208866 TeV)

Two atomic clocks are synchronized while on Earth before one is launched (within a GPS satellite) into a medium-altitude Earth orbit. The satellite orbits the Earth at an altitude of 22,000 km, with an orbital velocity of 15,000 km/hr. After 1000 orbits, estimate the time difference between the two atomic clocks? (Assume that only special relativity effects are present.)

ANS: (~4 x 10-3s)

A wooden chest is pulled across a level ship's deck by a force of 2.20E2 N. If the chest accelerates at 0.488 m/s² and coefficient of friction between the object and the deck is 0.310, what is the mass of the wooden chest?

On a foggy day, two drivers spot each other when they are 80m apart. they are travelling at 72km/h and 60km/h. both of them simultaneously apply brakes which retards both the cars at a rate of 5m/s^2. determine whether they avert collision or not?

https://drive.google.com/file/d/0B1f-P0kkAkRVQ3BmRTZxRTRaUi1wb2lPSXR2ZzBjRFpYRHFV/edit?usp=sharing

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