Calculate the length of the rocket according to X.

A space shuttle is released from the rocket. The shuttle moves with speed 0.20c to the right according to X. Calculate the velocity of the shuttle relative to the rocket.

the time interval between the lamps turning on.

which lamp turns on first.

On the diagram label the coordinates x and ct.

State and explain whether the ct coordinate in (c)(i) is less than, equal to or greater than 1.0 m.

Calculate the value of c ²t ² – x ².

the gamma factor is \(\frac{5}{3}\) or 1.67

L = \(\frac{{450}}{{\frac{5}{3}}}\) = 270 «m»

Allow ECF from MP1 to MP2.

[2 marks]

u' = «\(\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}} = \)» \(\frac{{0.20c - 0.80c}}{{1 - 0.20 \times 0.80}}\)
OR
0.2c = \( = \frac{{0.80c + u'}}{{1 + 0.80u'}}\)

u' =  «–»0.71c

Check signs and values carefully.

[2 marks]

Δt' = «\(\gamma \left( {\Delta t - \frac{{v\Delta x}}{{{c^2}}}} \right) = \)» \(\frac{5}{3} \times \left( {0 - \frac{{\left( {0.80c \times 9000} \right)}}{{{c^2}}}} \right)\)

Δt' = «–»4.0 x 10^–5 «s»

Allow ECF for use of wrong \(\gamma \) from (a)(i).

[2 marks]

lamp 2 turns on first

Ignore any explanation

[1 mark]

x coordinate as shown

ct coordinate as shown

Labels must be clear and unambiguous.

Construction lines are optional.

[2 marks]

«in any other frame» ct is greater

the interval ct' = 1.0 «m» is proper time
OR
ct is a dilated time
OR
ct = \(\gamma \)ct' «= \(\gamma \)»

MP1 is a statement

MP2 is an explanation

[2 marks]

use of c ²t ² – x ² =  c ²t' ² – x' ²

c ²t ² – x ² = 1² – 0² = 1 «m²»

for MP1 equation must be used.

Award [2] for correct answer that first finds x (1.33 m) and ct (1.66 m)

[2 marks]