Arianna kicks a soccer ball off the ground and into the air with an initial velocity of 42 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach?

1 Answer
A08
Jul 14, 2016

#approx27.6ft#

Explanation:

Kinematic equation connecting various quantities of interest is
#v^2-u^2=2gh#
where #v# is final velocity, #u# is initial velocity, #g# is acceleration due to gravity#=32fts^-2 and h# is height reached.

Given initial height #=0ft#
At maximum height #h_"max"#, #v=0#

Inserting various values in the equation we get
#-(42)^2=2xx(-32)h_"max"#
#-ve# sign in front of #g# indicates that gravity is acting in a direction opposing the motion. Solving for #h_"max"# we get

#h_"max"=(42)^2/64#
#=>h_"max"approx27.6ft#

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