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Problem 45 Hard Difficulty

Owen and Dina are at rest in frame $\mathrm{S}^{\prime}$ , which is moving with a speed of 0.600$c$ with respect to frame $\mathrm{S}$ . They play a game of catch while Ed, at rest in frame $\mathrm{S}$ , watches the action (Fig. P26.45) . Owen throws the ball to Dina with a speed of 0.800 $c$ (according to Owen) and their separation (measured in $\mathrm{S}^{\prime} )$ is equal to $1.80 \times 10^{12} \mathrm{m} .$ (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, and (d) how fast is the ball moving?

Answer

a) $-0.800 c$
b) $7.50 \times 10^{3} s$
c) $1.44 \times 10^{12} m$
d) $-0.385 c$

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Video Transcript

Let's to part here. Well, Dean is at rest relative to open. Hot Dina is a trust eight rest relative. Relative two Oh, man. And therefore, according to Dina, the ball is going, eh? Minus zero point e signal zero times the speed of light. Uh, so, um, with respect to or according to Dina, the bullies Morning. So according according to dina at the ball, the ball is moving the ball is mourning eight minus 0.80 zero times the speed of light R b When we know they over time is equal to proper land divided by speed. We have proper land, which is 1.80 multiplied by tend to the power 12 divided by we. Well, we 0.80 z don't move to blind eye are three. Multiply by 10 to the power eight. In dividing the two numbers, we get 7.5 cereal multiply by 10 to the power. Three seconds. Artsy Well, we know it contracted land. Elyse called to proper lynch wanted like I square root off one minus b squared, divided by C square. Let's play in. Plug in the values we have probably meant which is 1.8. Multiply by 10 to the power 12. Multiply by square root off one minus. We have 0.600 all scripts, six grand gets cancelled it C square and therefore contracted. Lance is equal to one point forward for multiply by 10 to the power 12 meters now a party. Well, uh, Bardi, you find out but lost you of the gold relative to uh huh um Badge Ben, we is equal to minus zero point, huh? 800 times the speed of light unless a 0.0 point 600 times the speed of light. Divided by, uh, one less minus 0.800 times the speed of light into 0.600 times the speed of light unsolved ing this weekend musical too. Minus 0.3 85 times the speed of light

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