A particle is projected from the point B on an incline plane at an angle of 3 7 ∘ from horizontal as shown in figure. If initial speed of particle is 20 m/s in horizontal direction then match the list

Question

A particle is projected from the point B on an incline plane at an angle of $3 7^{\circ}$ from horizontal as shown in figure. If initial speed of particle is 20 m/s in horizontal direction then match the list-I with list-II. (Take $g = 10 m / s^{2}$ )

List-I	List-II
(I) Time when particle hits the incline plane is t then the value of "5t" (in seconds)	(P) 30
(II) Range (along incline) of the projectile (in m) is	(Q) 4
(III) Horizontal distance AC (in m) is	(R) 15
(IV) Magnitude of vertical component of velocity of the particle (in m/s) when it hit the incline plane is nearly	(S) 75
	(T) 2

TestHub · Accepted Answer

Horizontal launch: x = 20 t , y = 5 t 2 downward. The particle hits the incline when y / x = tan 3 7 ∘ = 3/4 , so 5 t 2 /20 t = 3/4 ⇒ t = 3 s. (I) 5 t = 15 -> R. (II) Range along incline: x / cos 3 7 ∘ = 60/0.8 = 75 m -> S. (III) Incline length AB = 80 m, so AC along incline = 5 m; horizontal distance A C = 5 cos 3 7 ∘ = 4 m -> Q. (IV) v y ​ = g t = 30 m/s -> P. Correct option: (C)

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