Question

A 1-pound ball and a 100-pound ball are dropped from a height of 10 feet at the same time. in the absence of air resistance, __________.

Answer 1

The 100 ball would fall faster

Answer 2

They both will reach the ground at the same time. it will be a tie

Step-by-step explanation:

Given

`m_1 = 1 lb\\\\m_2 = 100 lb\\\\height,h = 10 ft\\\\`

Known

acceleration due to gravity,
`g = 32.2 ft/s^2\\`

Solution

Since the balls are dropped freely, their inital velocity u is zero.

let us find the final velocity of 1 pound ball

`v^2=-u^2 + 2gh\\\\v^2 = 0^2 + 2 * 32.2 * 10\\\\v^2 = 196\\\\v = 25.4 ft/s`

Note that in the equation is
`v^2=-u^2 + 2gh` the mass of the object has no place. So, The final velocity is independent of the mass

so the final velocity of the 100 pound ball will also be 25.4 ft/s

Now let us find the time taken for the 1 pound ball

`v = u + gt\\\\25.4 = 0+ 32.2t\\\\t = 0.788s`

Since the equation
`v = u + gt` does not depend on mass, the 100 pound ball will also reach the ground at time t = 0.788 s