A gun kept on a striaght horizontal is used to hit a car, traveling along the same road away form the gun with a unfrom speed `20 m//s`. The car is at a distance 0f `160 m` from the gun, when the gun is fired at an angle of `45^(@)` with the horizontal Find the distance of the car from the gun when the shell hits it and the speed of projection of the shell from the gun.

Explanation

The speed of the car v=`72xx(5//18)=20m//s`
The time of flight of projectile

T`=(2u sin theta)/(g)=(usqrt(2))/(g) ["as" theta=45^(@)]`
and range of projectile `R=(u^(2) sin 2theta)/(g)=(u^(2))/(g)`
According to given problem.
`R=500+vT`
Substituting the values of T and R from Eqns. (i) and (ii) in the above,
`(u^(2))/(g)=500+(usqrt(2))/(g)xx20`
or `u^(2)-20sqrt(2)u-4900=0`
or `u=(1//2)(20sqrt(2)+-sqrt((800+4xx4900))]`
or `u=10(sqrt(2)+-sqrt(51)]`
As negative sign is physically unacceptable,
`u=10[1.414+7.141]=85.56m//s`
Substituting the above value of u in Eqn. (ii).
`R=(u^(2))/(g)=((85.56)^(2))/(9.8)=746.9m`.