Free Fall UAM Question

Question

A book is thrown upward from 2.13 m beneath a shelf. It stays in the air for 1.76 s traveling above the shelf and then falling back onto the shelf (ignore any translational movement). How fast is it going when it lands the shelf?

Answer 1

Since you are given the displacement, time, and g = 9.8 m/s²,

use Δy = ½(v_i + v_f)t and v_f = v_i + at to solve for v_f.

 

 

Rearranging the two equations,

 

v_f + v_i = 2Δy/t

 

v_f - v_i = -gt

 

 

 

Adding, 2v_f = 2Δy/t - gt

 

 

v_f = Δy/t -gt/2 = 2.13/1.76 - 9.8*1.76 = -16.0 m/s

 

 

The minus sign indicates that the book is moving downward when it hits the table.