Question

a bullet plunges vertically into a retarding medium with an initial velocity u. its velocity is reduced by 20% in a distance of 0.9m in the medium if a is the uniform retardation in the medium then

the distance is 2.5

the distance is 1.6

its avg velocity is root5a/2

the time of travel in the medium is root 5/a


there are one or more answers correct

Answer 1

the equation of motion here is
\[x= x _{0}+v _{0}t-at ^{2}/2\]

Answer 2

what x0

Answer 3

\[x _{0}=0\]
\[v _{0}=u _{0}\]

Answer 4

ok,,,,,,,,then

Answer 5

Next you must calculate acceleration using info about movement of first 20% of distance

Answer 6

and motion equation

Answer 7

then you will get acceleration in terms of u0

Answer 8

stop there is an easier way to find acceleration

Answer 9

\[a=(v _{f}-v _{i})/t\]

Answer 10

for the first 20% of path
vf=0.8u0
vi=u0

Answer 11

ok

Answer 12

then

Answer 13

put the acceleration expression in motion equation and get the result

Answer 14

hey how vf=0.8u0 i think 0.9

Answer 15

its velocity is reduced by 20% in a distance of 0.9m

Answer 16

so it is 0.18

Answer 17

No velocity reduced by 20% means that it is initially was 100 % U0 then it became 80%U0=0.8U0. See?

Answer 18

ok

Answer 19

go on

Answer 20

got it)))

Answer 21

the answer is a

Answer 22

for this question there is more than one answer we have to find all of them we have to check each and every options

Answer 23

ok
a=(vf-vi)/t
so
let's assume that first 0.9m of path was travelled during t1
a = -0.2U0/t1

Answer 24

and put it in motion equation

Answer 25

ok

Answer 26

can u write whole answer completely so it will be easy to understand

Answer 27

then you will get
\[0.9 m = u_{0}t_{1}-(u_{0}/5t_{1})t_{1}^2/2\]
\[t_{1}=1m/u_{0}\]
but \[a=-u_{0}/5t_{1}\]
now
\[a=u_{0}/5m\]
next
\[v=v_{0}+at=v_{0}-(u_{0}/5m)t\]
we know that when bullet stops at
\[t_{final}\]
its speed is zero so
\[0=v_{0}+at=v_{0}-(u_{0}/5m)t_{final}\]
we get
\[t_{final}=5m/u_{0}\]
now
you are ready to find the whole distance traveled by bullet during time interval
\[t_{final}\]
try to solve it yourself

Answer 28

thanxx

Answer 29

Not at all!

Answer 30

Let's try to find if another options are correct

Answer 31

oops
\[a=-u_{0}^2/5m\]

Answer 32

ok

Answer 33

the second option is not correct because the distance is different.
the third and fourth option are obviously not correct because you can't take root of the negative value.

Answer 34

the answer for this is a c d

Answer 35

c is correct only when the sign of a is "+"

Answer 36

ok

Answer 37

the same with d