word problem

Question

A student designs a container as part of an egg drop. She believes the egg can withstand a fall as long as the speed doesn't exceed 80ft/s. She uses equation v=square root of ((V₀)²+2ad) to model the velocity,v in feet per second, as a function of constant acceleration, a, in feet per second squared and the drop distance d, in feet. Assuming the students specifications are correct, will the egg break if student drops it from 5 feet? From 80 feet? What's the maximum height the egg can be dropped? (The acceleration due to gravity is 32ft/s²)

Answer 1

v² - v₀² = 2gd

 

v = √(2gd + v₀²)

 

It is easier if you answer the last question first.  Find the maximum height d that keeps v ≤ 80 ft/s.  I will assume the object is released from rest, which makes v₀ = 0 ft/s.  Then set

 

v_max = √(2gd_max) ⇒ 

 

d_max = v_max² / (2g) = (80)² / [2(32)] ft = 100 ft

 

It breaks if it is released from rest at a height above 100 ft.