Question

a particle is projected horizontaly with a speed u from the top of a plane inclided at an angle thita with the horizontak how far from the point of projection will the particle strike the plain​

Answer 1

Answer:

2u2gtanθsec is your answer..

Explanation:

Suppose that the particle strikes the plane at a point P with corrdinates (x,y). Consider the motion between points A and P by resolving them into two directions

Motion in x-direction

Initial velocity =u,

acceleration =0

∴x=ut...(i)

Motion in y-direction

Initial velocity =0,

acceleration =g,

y=(½)gt2...(ii)

Eliminating t from (i) & (ii)

y=12g(x2)u2

Also, y=xtanθ

Therefore gx22u2=xtanθ⇒gx22u2−xtanθ=0

⇒x(gx2u2−tanθ)=0⇒x2u2tanθg...(iii)

Thus, y=xtanθ=2u2tan2θg...(iv)

∴ Distance AP=x2+y2−−−−−−√=2u2gtanθ

=(1+tan2θ)−−−−−−−−−−√=2u2gtanθsec

Hope It Helps

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