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Question

A particle is projected at an angle of 30 with an inclined plane calculate as shown in figure.

(i) Time of flight of particle.

(ii) Distance traveled by particle (AB) along the inclined plane


A

Time of flight = 125sec

Distance along incline = 125(863)m

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B

Time of flight = 2 sec

Distance along incline = 16 m

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C

Time of flight = 3 sec

Distance along incline = 6 m

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D

Time of flight = 125sec

Distance along incline = (863)m

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Solution

The correct option is A

Time of flight = 125sec

Distance along incline = 125(863)m


(i) To find out time of flight here, we can analyze the motion in y-direction; we can use the formula y=uyt+12ayt2. By analyzing motion in y-direction , the displacement of the particle in y-direction during motion is zero.

Now uy=usin α=u.sin 37=35×10=6 ms

ay=gcos θ=gcos 60=10×12=5 ms

So, y=u1t+12ayt20=6t52t2t=125S

(ii) To find out the distance traveled along AB, we have to analyze the motion in x-direction. So we have to use the formula

x=uxt+12axt2

Here ux=ucos α=10cos 37=10×45=8 ms,ax=gsin θ=10sin 60=10×32=53 ms

And t=125s, x=8×12512.53(125)2=965532×14425=9657235=125(863)m


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