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Old Aug 15th 2009, 07:41 AM   #1
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Questions about relative velocity - basic

1. Imagine that you are in a space shuttle moving at a speed of 0.8 times the speed of light (i.e. 0.8 c) relative to the ground and a beam of light is shone past you in the opposite direction. What is the speed of the beam of light that has passed you? (Select the option(s) that apply)

A. 0.2 c relative to the ground
B. 0.2 c relative to you
C. 1.8 c relative to you
D. 1 c relative to the ground
E. 1 c relative to you
2. Consider a situation where you are driving a car and moving along a straight road at a speed of 80 km/h with respect to your friend who is sitting at a bus stop along the road. A sports car zooms pass you, travelling in the same direction as you. According to your friend, the car is moving at 150 km/h
What is the speed of your car as observed by the driver driving the sports car?

3. Suppose you are standing still on an infinitely flat stationary ground and your friend is travelling in a spaceship at 98% speed of light horizontally according to you. Your friend has a stopwatch and he starts the stopwatch at the instant when he zooms past you. After a while your friend stops his spaceship instantly. At the same time, he notes down the time interval registered on his stopwatch. If the distance between you and his spaceship (after it stops) is 1477.4 km, what is the time interval noted down by your friend on his stopwatch?
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Old Aug 15th 2009, 09:37 AM   #2
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Have you attempted these questions?

1. Use the velocity composite rule.

$\displaystyle v = \frac {c^2(V_a + V_b)}{c^2 + (V_a)(V_b)}$

2. $\displaystyle V_c = V_a - V_c$


3. Time dilation equation.

$\displaystyle \frac {d}{v}' = \frac {\frac {d}{v}}{\sqrt { 1 - \frac {v^2}{c^2}}}$
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Last edited by Deco; Aug 16th 2009 at 09:48 AM.
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Old Aug 15th 2009, 08:59 PM   #3
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is the second formula correct?
why is Vc repeated?
Vc = Va - Vc?
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Old Aug 15th 2009, 09:00 PM   #4
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Make it

V_r = V_a - V_c
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Old Aug 15th 2009, 09:02 PM   #5
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oh..okay.
but can i ask what is r, a and c in this qn?
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Old Aug 15th 2009, 09:03 PM   #6
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V_r is the observed velocity.

V_a is velocity of object A.

V_c is velocity of object C.
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Old Aug 15th 2009, 09:12 PM   #7
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so can i say the answer for that qn is
Vr = 150 - 80 = 70km/h?
is the working correct?
the answer is indeed 70 but i aint sure whether is it the correct way of solving...
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Old Aug 15th 2009, 09:16 PM   #8
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Yes, it is correct. Remember it is a absolute value, the sign has no real significance.
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Old Aug 15th 2009, 10:30 PM   #9
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i got no idea how to do question 1 and 3 at all.
though u have provided the formula for those, but i still dont know how to start.
can you teach me?. thanks.
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Old Aug 15th 2009, 11:05 PM   #10
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So for the first question we let,

V_a = velocity of spacship = 0.8c

V_b = velocity of the light passing you = c

Now, just plug it in:


$\displaystyle
v = \frac {c^2(V_a + V_b)}{c^2 + (V_a)(V_b)}
$

$\displaystyle v = \frac {c^2 (c + 0.8 c)}{c^2 + (0.8c)(c)}$

$\displaystyle v = \frac { 1.8c^3}{1.8c^2}$

$\displaystyle \boxed {v = c}$-----(E).
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Last edited by Deco; Aug 16th 2009 at 09:41 AM.
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