A projectile is projected in x - y plane with velocity v0. At top most point of its trajectory projectile explodes into two identical fragments. Both the the fragments land simultaneously on ground and stick there. Taking point of projection as origin and R as range of projectile if explosion had not taken place. Which of the following can not be position vectors of two pieces, when they land on ground.

Engineering

Physics

Center of Mass

Projectile Motion

Momentum and Energy Conservation for System of Particles

Question

A projectile is projected in x - y plane with velocity v₀. At top most point of its trajectory projectile explodes into two identical fragments. Both the the fragments land simultaneously on ground and stick there. Taking point of projection as origin and R as range of projectile if explosion had not taken place. Which of the following can not be position vectors of two pieces, when they land on ground.

$0 \hat{i}, 2 R \hat{i}$

$\frac{R}{2} \hat{i}, \frac{3 R}{2} \hat{i}$

$2 Ri + \frac{R}{2} \hat{k}, R \hat{i} - \frac{R}{2} \hat{k}$

$R \hat{i} - R \hat{k}, R \hat{i} + R \hat{k}$

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Trajectory of CM is not changed due to explosion.

${\vec{r}}_{CM} = \frac{m {\vec{r}}_{1} + m {\vec{r}}_{2}}{m + m} = \frac{{\vec{r}}_{1} + {\vec{r}}_{2}}{2}$

Here ${\vec{r}}_{CM} = R \hat{i}$ .