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An-earth-based-observer-sees-rocket-A-moving-at-0-70c-directly-towards-rocket-B-which-is-moving-towards-A-at-0-80c-How-fast-does-rocket-A-sees-rocket-B-approaching-




Question Number 59780 by necx1 last updated on 14/May/19
An earth-based observer sees rocket A  moving at 0.70c directly towards rocket  B,which is moving towards A at 0.80c.  How fast does rocket A sees rocket B  approaching?
$${An}\:{earth}-{based}\:{observer}\:{sees}\:{rocket}\:{A} \\ $$$${moving}\:{at}\:\mathrm{0}.\mathrm{70}{c}\:{directly}\:{towards}\:{rocket} \\ $$$${B},{which}\:{is}\:{moving}\:{towards}\:{A}\:{at}\:\mathrm{0}.\mathrm{80}{c}. \\ $$$${How}\:{fast}\:{does}\:{rocket}\:{A}\:{sees}\:{rocket}\:{B} \\ $$$${approaching}? \\ $$$$ \\ $$
Answered by ajfour last updated on 14/May/19
v_(rel) = ((0.7c+0.8c)/(1+0.56)) ≈ 0.9615c
$$\mathrm{v}_{\mathrm{rel}} =\:\frac{\mathrm{0}.\mathrm{7c}+\mathrm{0}.\mathrm{8c}}{\mathrm{1}+\mathrm{0}.\mathrm{56}}\:\approx\:\mathrm{0}.\mathrm{9615c} \\ $$

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