A projectile is projected with a linear momentum p making an angle θ with the horizontal. The change in momentum of the projectile on return to the ground will be

Question

A projectile is projected with a linear momentum p making an angle θ with the horizontal. The change in momentum of the projectile on return to the ground will be (A)  2p tan θ  (B)  2p sin θ  (C)  2p cos θ  (D)  ~2p

Tardigrade Admin · Accepted Answer

mid( P f- P i)= mid Change in momentum <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/78f88ae383eccaaac23bcad4e08264b7-.png" /> =√P2+P2+2 P ⋅ P cos (π-2 θ) =P √2+2(- cos θ) =P √2(2 sin 2 θ) =2 P sin θ

Q. A projectile is projected with a linear momentum $p$ making an angle $θ$ with the horizontal. The change in momentum of the projectile on return to the ground will be

$2 p tan θ$

$2 p sin θ$

$2 p cos θ$

$2 p$

$∣ (P_{f} - P_{i}) =∣$ Change in momentum

$= P^{2} + P^{2} + 2 P \cdot P cos (π - 2 θ)$
$= P 2 + 2 (- cos θ)$
$= P 2 (2 sin^{2} θ)$
$= 2 P sin θ$

Q. A projectile is projected with a linear momentum p making an angle θ with the horizontal. The change in momentum of the projectile on return to the ground will be

2ptanθ

2psinθ

2pcosθ

2p