The punter stands on the 22 yard (roughly a meter) line to the left of the 50 yard line and the ball is kicked with an initial velocity of 25.3 m/s at an angle of 58.5° above the ground. How high does the punt go?

1 Answer
Meave60
Sep 26, 2015

The maximum height of the football is #23.8# m.

Explanation:

The maximum height of the football occurs halfway through its trajectory. The total hang time has been previously determined to be #t=4.40"s"#. The maximum height would occur at #t=2.20"s"#.

The equation to use is #y_"max"=v_"iy"t"+1/2 g"t"^2#, where:
#y_"max"="maximum height"#
#v_"iy"=v_"i"*sin58.5^"o"=21.6"m/s"#
#t=2.20"s"#
#"g=-9.8 m/s"^2"#

#y_"max"=21.6"m/s"*2.20"s"+1/2(-9.8"m/s"^2")(2.20s)"^2"#

#y_"max"=47.5"m"+1/2(-9.81"m/s"^2)(4.84"s"^2)=#

#y_"max"=47.5"m"-23.7"m"=#

#y_"max"=23.8"m"#

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