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3-2.Motion in Plane
normal
Average velocity of a particle is projectile motion between its starting point and the highest point of its trajectory is : (projection speed = $u$, angle of projection from horizontal= $\theta$)
A
$u\,\, cos\theta$
B
$\frac{u}{2}\sqrt {1 + 3{{\cos }^2}\theta } $
C
$\frac{u}{2}\sqrt {2 + {{\cos }^2}\theta }$
D
$\frac{u}{2}\sqrt {1 + {{\cos }^2}\theta }$
Solution
Displacement $=\sqrt{\left(\frac{R}{2}\right)^{2}+H^{2}}$
$R=\frac{u^{2} \sin 2 \theta}{g}$
$H=\frac{u^{2} \sin ^{2} \theta}{g}$
$t=\frac{T}{2}=\frac{u \sin \theta}{g}$
$\left|V_{a v g}\right|=\frac{| \text {displacement} |}{t}=\frac{u^{2} \sin \theta}{g} \sqrt{4 \cos ^{2} \theta+\sin ^{2} \theta} \sqrt{\frac{1}{4}} \frac{1}{\frac{u \sin \theta}{g}}$
$=\frac{u}{2} \sqrt{1+3 \cos ^{2} \theta}$
Standard 11
Physics
