Question

IIT 1974

Answer 1

A gun on a straight horizontal road is used to hit a car, travelling along the same road way from the gun with a uniform speed of 72 * (root 2) km/h. The car is at a distance of 50 m from the gun, when the gun is fired at an angle of 45 degrees with the horizontal.

Find:-
(i) The distance of the car from the gun when the shell hit it
(ii)The speed of projection of the shell from the gun

Answer 2

@ganeshie8 @BSwan

Answer 3

range = 50 + 72sqrt(2)*t = ucos(45)*t
time of flight, t = 2usin(45)/g

Answer 4

two equations, two unknowns
you can solve them

Answer 5

Wait let me grasp it

Answer 6

http://www.wolframalpha.com/input/?i=solve+50+%2B++72sqrt%282%29*t+%3D+u*cos%2845%29*t%2C+t+%3D+2usin%2845%29%2F10

t = 20.8 seconds
u = 147.4 m/s

Answer 7

only there is one thing i dint understand
is the car moving tward the gun or in the oposite direction ?

Answer 8

use the value of `t` to find the distance between gun and car

Answer 9

car is moving away from gun, @BSwan

Answer 10

t*u is the first answer ?

Answer 11

just multiply \(t\) by the speed of car

Answer 12

and add 50

Answer 13

wait a sec, we made a terrible mistake -
we overlooked the units :/

Answer 14

72 * (root 2) km/h need to be converted to m/s first

Answer 15

km/hr

Answer 16

http://www.wolframalpha.com/input/?i=solve+50+%2B++72sqrt%282%29*1000%2F%2860*60%29*t+%3D+u*cos%2845%29*t%2C+t+%3D+2usin%2845%29%2F10

Answer 17

yeah nice trick by this shrewd people

Answer 18

\(u = 50 m/s\)

\(t = 5\sqrt{2} s\)

Answer 19

yes

Answer 20

haha we need to watch out units always lol

Answer 21

seriously units can decide a person's career.

Answer 22

Now coming back to the problem

Answer 23

for the first part :
distance between gun and car = 50 + [72sqrt(2) (1000/(60*60))*5sqrt(2)]

Answer 24

for the second part :
u = 50 m/s

Answer 25

Yes 250 and 50 . great

Answer 26

Looks good ^

Answer 27

explain to @BSwan , why car is going away from gun... @No.name

Answer 28

naa forget it

Answer 29

If it was approaching the gun then wouldn't the bullet go over the car lol

Answer 30

@BSwan

Answer 31

The angle of the bullet fired isn't changing

Answer 32

So if the car was appraching the gun then the question wouldn't make sense
is that the logic @ganeshie8

Answer 33

nope, the question is fine either ways - recall the previous problem we did when the guy runs towards the projectile to catch it ?

Answer 34

Is it with the range

Answer 35

no lol, the reason is this :
In the question itself, we're explicitly given that the car is going away from the gun

Answer 36

"away from the gun"

Answer 37

we will get a different and a valid answer if do it the other way

Answer 38

travelling along the same road way from the gun
ohh ohk so its travelling from
i dintnote from

Answer 39

No it is clearly given in the question away from the gun

Answer 40

yeah

Answer 41

@BSwan , "a" is missing in the question :)

travelling along the same road \(\color{red}{a}\)way from the gun
ohh ohk so its travelling from
i dintnote from

Answer 42

a is missing typo

Answer 43

ohk -,-
ty for clear my doubts

Answer 44

No problem