At t = 0 on the planet Gravitus Increasicus, a projectile is fired with speed v0 at an angle θ above the horizontal. This planet is a strange one, in that the acceleration due to gravity increases linearly with time, starting with a value of zero when the projectile is fired. In other words, g(t) = βt, where β is a given constant. What horizontal distance does the projectile travel? What should θ be to maximize this distance?

{Answer is not there because it is copied from "Introduction to classical mechanics by David Morin", it here because it is on eof hardest one. Problem-3.43}

The coordinate of a point moving rectilinerly along the x-axis changes in time according to the law \(x = 17 + 9t + 41t^2\)  where x is in cm and t is in sec. The velocity and acceleration at t=.075sec is (respectively) are-

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