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who enters the water first? by how much? in a diving siblings showcase, 11-year-old...

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mgoun | Student, Undergraduate | (Level 1) Valedictorian

Posted October 16, 2012 at 10:35 PM via web

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who enters the water first? by how much? 

in a diving siblings showcase, 11-year-old hannah takes off from a 24.61 foot platform with an initial velocity of 9.7 ft/sec at the same time that her brother tyler, who is 3.5 years older, takes off from a 32.81 foot platform with an initial velocity of 4.51 ft/sec.

round to the nearest hundredth.

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lfryerda | High School Teacher | (Level 2) Educator

Posted October 17, 2012 at 12:49 AM (Answer #1)

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The height formula for constant gravity is 

`h=-1/2g t^2+v_0t+h_0`

where g=32 ft/sec^2 is the acceleration due to gravity, `v_0` is the initial velocity and `h_0` is the initial height.

For Hannah, the equation of height is:


and Tyler has the equation for height of 


To find when they hit the water, use the quadratic formula, where only the negative roots are used to end up with positive time values.

For Hannah, 



For Tyler,



To the nearest hundredth, both Hannah and Tyler hit the water at the same time.

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