Mechanics | Relativity Answers

a policeman chasing an outlaw escaping on car moving at a speed of 3/4c , the police officer fires a bullet from the pursuit car which only goes half of speed of light . the muzzle velocity of bullet relative to gun is 1/3c . will bullet reach its target
according to galileo and einsteins

A block of wood weighs 60g in air. A lead sinker weighs 70g in water. The sinker is attached to the wood and both together weighs 65g in water. Find the the relative density of the wood.

Receiving two negative values of T in suvat problem when I shouldn't be.

Problem is: A ball is accelerating at a constant rate of 2.54 m*s^-2. After traveling 850 meters it is going at a velocity of 78.19 m*s^-2. How long has the ball been traveling?

My solution: s = vt -1/2at^2 ⇔ 1/2 at^2 -vt +s = 0⇔ t=-v-(v^2 - 2as)/a or -v +(v^2 - 2as)/a

t =(-78.19 - sqrt(78.19^2 -2*2.54*850))/2.54) or (-78.19 + sqrt(78.19^2 -2*2.54*850))/2.54)

from there I get -47.467 or -14.100

Neither of these make sense to me within the context of the problem

F=KAV/R Find the dimension for K given A=Area V=Velocity R=Radius

(1)
A car travels around a bend of radius 400m on a road which is banked at an angle to the horizontal, if the car has no tendency to slip when travelling at 35m/s. Find the angle ..

By expanding equations (3.6) and (3.7) in a Taylor series, show that the
Newtonian and relativistic effects agree to first order in v
c =
vS−vR
c
. This
means that engineers who design radar devices do not in fact need to un-
derstand relativity. You can do this using the expansions from problem
(2-2). Note that “to first order” means that we ignore any terms propor-
tional to v
2
, v2
R, v2
S
or higher powers of v, vR, vS.

The most common use of relativity in every day life involves what is called
the ‘Doppler effect.’ This is an effect in which the frequency (= rate at
which crests pass by you) of a wave depends on the reference frame. There
is also a Doppler effect in Newtonian physics, but Newtonian physics would
predict a different amount of the effect. The Doppler effect is used in
various devices such as ‘Doppler radar’ and police radar guns to measure
the speed of storm systems or cars. For this problem, derive the formula
for the relativistic Doppler effect
τR =
r
c + v
c − v
τS . (3.6)
where v is the velocity of the source (S) away from the receiver (R). Here,
I have expressed the formula using the period τ (the time between wave
crests) as measured by each observer.

What happens in the relativistic addition of velocities formula (derived in
problem (10) when one of the velocities (say, vBA) is the speed of light??

. What happens in the relativistic addition of velocities formula (derived
in problem (10) when the two velocities are both very small? Try it for
vBA = .01c and vA = .01c. How much does the relativistic result differ
from the Newtonian result (1.2) in this case?

The starting point for our discussion of relativity was the observation that
velocities do not combine in the naive way by just adding together. Clearly
then, a good question is “just how do they combine?” In this problem, you
will derive the formula for the ‘relativistic composition of velocities.’ Let
me point out that you have all of the tools with which to do this, since you
know how to translate both distances and times between reference frames.
This is just a quantitative version of problem (3-8), but we now work in
the more general case where vAB is arbitrary. Feel free to choose units so
that c = 1. Then you can ignore all the factors of c to make the algebra
easier.