The initial vertical velocity of a rocket shot straight up is 42 meters per second. how long does it take for the rocket to return to earth? round your answer to the nearest tenth of a second. show all your work.

It takes 4.3 seconds for the rocket to return to earth.

The equation is:

where -9.8m/sec² is the acceleration due to gravity, v₀ is the initial velocity, and h₀ is the initial height.  We will go from the assumption that the rocket is launched from the ground, so h₀=0, and we are told that the initial velocity, v₀, is 42.  This gives us:



We will use the quadratic formula to solve this.  The quadratic formula is:


Plugging in our information we have:


x=0 is when the rocket is launched; x=4.3 is when the rocket lands.

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