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
Time of flight = 125sec
Distance along incline = 125(8−6√3)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+12ayt2⇒0=6t−52t2⇒t=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=−5√3 ms
And t=125s, x=8×125−12.5√3(125)2=965−5√32×14425=965−72√35=125(8−6√3)m