Question

Wo baseballs are fired into a pile of hay. If one has twice the speed of the other, how much farther does the faster baseball penetrate?

Answer 1

Step-by-step explanation:

Given

Two baseballs are fired into a pile of hay such that one has twice the speed of the other.

suppose u is the velocity of first baseball

so velocity of second ball is 2u

suppose
`d_1` and
`d_2` are the penetration by first and second ball

using
`v^2-u^2=2 ad`

where v=final velocity

u=initial velocity

a=acceleration

d=displacement

here v=0 because ball finally stops

`0-u^2=2ad_1----1`

for second ball

`0-(2u)^2=2ad_2----2`

divide 1 and 2 we get

`(u^2)/(4u^2)=(d_1)/(d_2)`

as deceleration provided by pile will be same

`(1)/(4)=(d_1)/(d_2)`

`d_2=4d_1`

thus faster ball penetrates 4 times of first ball