Question

a particle of mass 1kg is projected at an angle 30 degree with horizontal with a velocity v= 40m/s . the change in linear momentum of the particle after time t = 1s will be(g= 10m/s) a) 7.5kg-m/s (b) 15kg-m/s (c)10kg-m/s (d) 20kg-m/s

Answer 1

intial velocity , $\vec{u}=40cos30^{\circ}\hat{i}+40sin30^{\circ}\hat{j}$
$\vec{u}=20\sqrt{3}\hat{i}+20\hat{j}$

after 1 sec , velocity of projectile is ,
$\vec{v}=ucos\theta\hat{i}+(usin\theta-gt)\hat{j}$
$\vec{v}=40cos30^{\circ}\hat{i}+(40sin30^{\circ}-10\times1)\hat{j}$
$\vec{v}=20\sqrt{3}\hat{i}+10\hat{j}$

now, change in linear momentum , ∆P
∆P =$P_f-P_i$
=m$(v_f-v_i)$
=m$\{(20\sqrt{3}\hat{i}+10\hat{j})-(20\sqrt{3}\hat{i}+20\hat{j})\}$
=$1kg\times(-10\hat{j})$
=$-10Kgm/s\hat{j}$

hence magnitude of change in linear momentum is 10 kgm/s .
therefore option (c) is correct