Find the time taken to reach given distance

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Reference no: EM131382889

A particle P of mass m is attracted towards a fixed origin O by a force of magnitude mγ /r³, where r is the distance of P from O and γ is a positive constant.

[It's gravity Jim, but not as we know it.] Initially, P is at a distance a from O, and is projected with speed u directly away from O. Show that P will escape to infinity if u² > γ/a².

For the case in which u² = γ /(2a²), show that the maximum distance from O achieved by P in the subsequent motion is a, and find the time taken to reach this distance.

Reference no: EM131382889

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