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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 | 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:

`h=-1/2(32)t^2+9.7t+24.61=-16t^2+9.7t+24.61`

and Tyler has the equation for height of 

`h=-16t^2+4.51t+32.81`

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, 

`t={-9.7-sqrt{9.7^2+4(16)(24.61)}}/{2(-16)}`

`=1.58`

For Tyler,

`t={-4.51-sqrt{4.51^2+4(16)(32.81)}}/{2(-16)}`

`=1.58`

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

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