A mechanism on Earth used to shoot down geosynchronous satellites that house laser-based weapons is finally perfected and propels golf balls at 0.94c. a) How far will a detector riding with the golf ball initially measure the distance to the satellite? [Geosynchronous satellites are placed 3.58x104 km above the surface of the Earth.] b) How much time will it take the golf ball to make the journey to the satellite in the Earth’s frame? How much time will it take in the golf ball’s frame?

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A mechanism on Earth used to shoot down geosynchronous satellites that house laser-based weapons is finally perfected and propels golf balls at 0.94c. a) How far will a detector riding with the golf ball initially measure the distance to the satellite? [Geosynchronous satellites are placed 3.58x104 km above the surface of the Earth.] b) How much time will it take the golf ball to make the journey to the satellite in the Earth’s frame? How much time will it take in the golf ball’s frame?

Physics
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@Jemurray3 do I use length contraction on this? if so , how?
Yes, for the first part. As straightforwardly as you possibly could... \[ L = L_0 \sqrt{1-v^2/c^2} \]
so L0 would be 3.58x10^4 ?

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Yes, the proper distance is measured in the earth frame because the geosynchronous satellites are at rest relative to the earth.
for b) do I do just normal calcuation using t= l/v then lorentz transform that t?
Yes. Alternatively, you could divide the contracted distance by the velocity.
oh I see, that works too Thank you for your help

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