1.

An astronaut drops a rock from the top of a crater on the moon. When the rock is halfway down to the bottom of the crater, its speed is what fraction of its final impact speed?

Answer»

`(1)/(4sqrt(2))`
`(1)/(4)`
`(1)/(2sqrt(2))`
`(1)/(sqrt(2))`

Solution :Because the rock has lost half of its gravitational energy, its KINETIC energy at the HALFWAY point is half of its kinetic energy at IMPACT. Since K is PROPORTIONAL to `v^(2),` if `K_("at halfway point")` is equal to `(1)/(2)K_("at impact")`, then the rock's speed at the halfway point is `sqrt((1)/(2))=(1)/(sqrt(2))` its speed at impact.


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