Question

(3rd time Asking) Please help me with these questions!!!

Answer 1

(a) Water balloon 1 has height at time
`t`

`h_1(t)=-16t^2-20t+110`

and water balloon 2 has height

`h_2(t)=-16t^2+75`

Both water balloons are moving straight downward, so their distance is equal to

`|h_1(t)-h_2(t)|=|(-16t^2-20t+110)-(-16t^2+65)|=|35-20t|`

(b) When both water balloons are at the same height, we have
`h_1(t)=h_2(t)`. So you could set both quadratic expressions equal to each other and solve for
`t`. Or you can use the fact that, when they're at the same height, the distance between them is 0. So using the expression from part (a), we have

`|35-20t|=0\implies 35-20t=0\implies 35=20t\implies t=(35)/(20)`

or 1.75 seconds after being thrown/dropped.

At this time, they are both at a height of
`h_1(1.75)=h_2(1.75)`:

`h_2(1.75)=-16(2.25)^2+75=26`

feet.

(c) The second and fourth statements are true.