Question

The acceleration due to gravity on Earth is 32 ft/sec2. A tomato is dropped from 100 feet above the ground. Give units in your answers. (a) At what speed does the tomato hit the ground? (b) How long does it take for the tomato to travel the last 10 feet? Give your answer as a decimal approximation with units.

Answer 1

Answer:

a) the final velocity is v=80 ft/s

b) the time required is 2.5 seconds

Step-by-step explanation:

The final velocity is related with the acceleration through

v² = v₀² + 2*g*h

where

v₀= initial velocity= 0 (dropped from test)

g = acceleration

h = height

replacing values

v² = v₀² + 2*g*h = 0² + 2*32 ft/s² * 100 ft = 6400  ft²/s²

then

v= √6400  ft²/s² = 80 ft/s

the tomato hit the ground at v=80 ft/s

h₀= h + v₀*t - 1/2*g*t²  

since h₀=0 ( initial height) and v₀=0

0= h - 1/2*g*t²  

t = √(2*h/g)

replacing values

t = √(2*h/g) = √(2*100 ft / 32 ft/s²) = 10/4 s =2.5 s

t =2.5 seconds