Question

The function E(d)=0.25d√ approximates the number of seconds it takes a dropped object to fall d feet on Earth. The function S(d)=0.2⋅E(d) approximates the number of seconds it takes a dropped object to fall d feet on the sun. How long (in seconds) does it take a dropped object to fall 80 feet on the sun? Round your answer to the nearest hundredth.

Answer 1

0.45 second

Explanation:

The number of seconds it takes a dropped object to fall d feet on Earth is given as:

E(d)=0.25√d

the number of seconds it takes a dropped object to fall d feet on the sun is given as:

S(d)=0.2⋅E(d)

Therefore

S(d)=0.2 × 0.25√d = 0.05√d

Given that it take a dropped object to fall 80 feet on the sun (i.e d = 80 feet), to calculate the time in seconds we use:

S(d) = 0.05√d

S(d) = 0.05 × √80 = 0.05 × 8.944 ≈ 0.45 s

It takes 0.45 second for a dropped object to fall 80 feet on the sun