### 30 Nov

Problem : A gun kept on a straight horizontal road is used to hit a car, travelling along the same road away from the gun with a uniform speed of 72 km/hr. The car is at a distance of 500 metre from the gun, when the gun is fired at an angle of 45? with the horizontal. Find
(a) the distance of the car from the gun when the shell hits it,
(b) the speed of the projection of the shell from the gun.

Solution : will be posted tomorrow

### 9 Comments

• Angshuman Ghosh November 30, 2010 at 12:50 pm

743 mtrs

• Angshuman Ghosh November 30, 2010 at 12:50 pm

743 m
86.25 m/s

• Sayyed nadeem November 30, 2010 at 2:58 pm

Distance:) 747m speed:) 85.56m/s

• durgesh November 30, 2010 at 5:00 pm

(i) 743.9m approx.
(ii) 86.25m/s approx.

• Well the first answer can be easily solved by noting that the bullet will hit the car as soon as the car comes in the bullet’s path hence the car travels 500m before getting hit.
Next, the distance travelled by the bullet will be 500(sqrt(2))
and the speed of the bullet is 20(sqrt(2))

• i think there are many answer of this question i do it through following manner
distance traveled by bullet from its initial position is v/sqrt(2)*t here v is velocity of bullet and t is time after which they strike.
distance traveled by car from position of gun is 0.5+72*t
car and bullet strike when v/sqrt(2)*t = 0.5+72*t thus there are many sets of answers for which its is correct
please send me its correct answer

• Abhishek December 1, 2010 at 1:11 am

I solved it in reverse order..

The bullet must reach the ground when it collides with the car. Therefore range of the bullet and total distance traveled by the car will be equal at the moment of collision.

Range (R) = 500 + (2usino/g * 20 m/s)

or, 2u(sq)/g = 500 + (2usino/g * 20 m/s)

Solving quadratic equation..

+ve u comes out to be 86.25 m/s

and distance travelled is simply 86.25(sq.) / g = 743.9 m

Final Answer :-

(a) 743.9 m
(b) 86.25 m/s or 310.5 kmph

Hope its right!

• Abhishek December 1, 2010 at 1:16 am

Hey your questions are quite good. But please do provide easier values for calculations.. for questions like above, its difficult to be fairly accurate without a calculator.

Cheers !
Abhishek
JEE-2012 Aspirant

• distance from gun = 746.7m using g=9.8m/s2
speed of shell = 85.51 m/s