Exercise 44 Page 69

We can use the formula h=-16t^2+ h_0 to approximate the time it takes for the balloon to hit the ground. Let's begin by identifying that h_0 is the initial height from which we are dropping the balloon. When the balloon impacts the ground is h. Therefore, we can substitute 0 for h and 40 for h_0. h=-16t^2+ h_0 ⇒ 0=-16t^2+ 40 Next, we can solve for t.

0=-16t^2+40

SubEqn

LHS-40=RHS-40

-40=-16t^2

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Solve for t

DivEqn

.LHS /(-16).=.RHS /(-16).

40/16=t^2

ReduceFrac

a/b=.a /8./.b /8.

5/2=t^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

±sqrt(5/2)=t

CalcRoot

Calculate root

± 1.58≈ t

RearrangeEqn

Rearrange equation

t ≈ ± 1.58

Mathematically our solution can be positive or negative. However, in this scenario, a negative solution does not make sense. Our solution must then be t≈ 1.58.