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Question

Two particles A and B are projected simultaneously form the two towers of height 10 m and 20m respectively. Particle A is projected with an initial speed of 102 at an angle at 45 with horizontal, while particle B is projected horizontally with speed 10 m/s. If they collide in air, what is the distance d between the towers?
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Solution

The height of particle A at any instant t is given as,

hA=10+uAsin450t12gt2
hA=10+102sin450t12gt2=10+10t12gt2

Similarly, height of particle B at any instant t is given as,

hB=2012gt2

At the collision, both the heights are equal.

10+10t12gt2=2012gt2t=1s

Horizontal distance moved by particle A in 1 second is,

xA=uAcos45o×t=102cos450×1=10m

Horizontal distance moved by particle B in 1 second is,

xB=uB×t=10×1=10m

d=xA+xB=10m+10m=20m

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