A projectile is fired with velocity u at an angle θ with horizontal. At the highest point of its trajectory it splits up into three segments of masses m, m and 2 m. First part falls vertically downward with zero initial velocity and second part returns via same path to the point of projection. The velocity of third part of mass 2 m just after explosion will be

Question

A projectile is fired with velocity u at an angle θ with horizontal. At the highest point of its trajectory it splits up into three segments of masses m, m and 2 m. First part falls vertically downward with zero initial velocity and second part returns via same path to the point of projection. The velocity of third part of mass 2 m just after explosion will be (A) u cos θ (B) (3/2) u cos θ (C) 2 u cos θ (D) (5/2) u cos θ

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/b74125623a45bcd0dcf2eb6758266d5a-.png" /> along x-axis no internal force exists, hence momentum will be conserved along x-axis ..Pi)x=Pf)x (m+m+2 m) cos θ=-m u cos θ+0+2 m V ⇒ 2 m v=5 m u cos θ v=(5/2) u cos θ and along y direction .Pi)y=0 So .Pf)y=0

$u cos θ$

$\frac{3}{2} u cos θ$

$2 u cos θ$

$\frac{5}{2} u cos θ$

along $x$ -axis no internal force exists, hence momentum will be conserved along $x$ -axis
$P_{i})_{x} = P_{f})_{x}$
$(m + m + 2 m) cos θ = - m u cos θ + 0 + 2 mV$
$\Rightarrow 2 m v = 5 m u cos θ$
$v = \frac{5}{2} u cos θ$
and along $y$ direction $P_{i})_{y} = 0$
So $P_{f})_{y} = 0$

ucosθ

23​ucosθ

2ucosθ

25​ucosθ

along x-axis no internal force exists, hence momentum will be conserved along x-axis Pi​)x​=Pf​)x​ (m+m+2m)cosθ=−mucosθ+0+2mV ⇒2mv=5mucosθ v=25​ucosθ and along y direction Pi​)y​=0 So Pf​)y​=0

$u cos θ$

$\frac{3}{2} u cos θ$

$2 u cos θ$

$\frac{5}{2} u cos θ$

along $x$ -axis no internal force exists, hence momentum will be conserved along $x$ -axis
$P_{i})_{x} = P_{f})_{x}$
$(m + m + 2 m) cos θ = - m u cos θ + 0 + 2 mV$
$\Rightarrow 2 m v = 5 m u cos θ$
$v = \frac{5}{2} u cos θ$
and along $y$ direction $P_{i})_{y} = 0$
So $P_{f})_{y} = 0$