1. Tardigrade
  2. Question
  3. Physics
  4. A particle A is projected from the ground with an initial velocity of 10 m s -1 at an angle of 60° with horizontal. From what height should another particle B be projected horizontally with velocity 5 m s -1 so that both the particles collide in ground at point C if both are projected simultaneously. (Take .g=10 m s -2)

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Q. A particle $A$ is projected from the ground with an initial velocity of $10\, m \,s ^{-1}$ at an angle of $60^{\circ}$ with horizontal. From what height should another particle $B$ be projected horizontally with velocity $5 \,m \,s ^{-1}$ so that both the particles collide in ground at point $C$ if both are projected simultaneously. (Take $\left.g=10 \,m \,s ^{-2}\right)$

Motion in a Plane

Solution:

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Both the particles will meet at $C$, if their time of flight is the same. The time of flight of $A$ is
$T=\frac{2 u \sin \theta}{g}$
$=\frac{2 \times 10 \times \sin 60^{\circ}}{10}=\sqrt{3} s$
For vertical downward motion of particle $B$ from $B$ to $C,$ we have
$h=\frac{1}{2} g T^{2}$
$=\frac{1}{2} \times 10 \times(\sqrt{3})^{2}=15 m$