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.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The height function for constant acceleration is `h=-1/2 g t^2+v_0t+h_0` where `v_0` is the initial velocity and `h_0` is the initial height.  

For both children, the time to enter the water is found by setting the height to zero and solving for t.

For Hannah, we need to find the time by solving:

`-1/2(32)t^2+9.7t+24.61=0`

`-16t^2+9.7t+24.61=0`   use quadratic formula

`t={-9.7-sqrt{9.7^2+4(24.61)(16)}}/{2(-16)}`   using negative root to keep time positive

`=1.58`

For Tyler, solve the equation:

`-1/2(32) t^2+4.51t+32.81=0`   

`-16t^2+4.51t+32.81=0`   use quadratic formula

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

`=1.58`

Within a hundredth of a second, both children enter the water at exactly the same time of 1.58 seconds after they jump.

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial