A shell is fired from a canon with a velocity v (m/s) at an angle θ with the horizontal direction. At the highest point…

Q: A shell is fired from a canon with a velocity v (m/s) at an angle θ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the canon and the speed (m/s) of the other pieces immediately after explosion is

(a)3 v cos θ

(b)2 v cos θ

(c)3/2v cos θ

(d)√(3/2)v cos θ

Ans: (a)

Sol: Let mass of shell = 2m and Speed of other piece = v’

Applying conservation of linear momentum ;

$\large 2 m \times v cos\theta = – m(v cos\theta) + m v’$

$\large v’ = 3 v cos\theta$