Question

if an average - sized man with a parachute jumps from an airplane, he will fall 12.5(0.2^t - 1)+20t feet in t seconds. how long will it take him to fall 142 feet? (round your answer)

Explanation:

Step1: Set up the equation

We set the distance - fall formula equal to 142. So, $12.5(0.2t - 1)+20t=142$.

Step2: Expand the equation

Expand $12.5(0.2t - 1)$ to get $12.5\times0.2t-12.5\times1 + 20t=142$, which simplifies to $2.5t-12.5 + 20t=142$.

Step3: Combine like - terms

Combine the $t$ terms: $(2.5t + 20t)-12.5=142$, so $22.5t-12.5 = 142$.

Step4: Isolate the term with $t$

Add 12.5 to both sides of the equation: $22.5t=142 + 12.5$, so $22.5t=154.5$.

Step5: Solve for $t$

Divide both sides by 22.5: $t=\frac{154.5}{22.5}\approx6.87$.

Answer:

$6.87$