Question

A body thrown up along a frictionless inclined plane of angle of inclination 30∘ covers a distance of 40 m along the plane. If the body id projected with the same speed at an angle of 30∘ with the ground, it will have a range of

(Take g=10 ms−2)

20 m

40 m

20√2 m

20√3 m

Solution

The correct option is **D**

20√3 m

Let u be the initial speed with which the body is thrown along the inclined plane. As shown in the figure , the effective deceleration is given by

a=gsin θ=g sin 30∘=g2=5 ms−2

Now, from the third equation of motion,

v2=u2−2as

⇒0=u2−2×5×40

⇒u=20 m/s

A projectile projected at angle θ=30∘ with this speed will have a range of

R=u2 sin 2 θg=20×20×sin 60∘10=20√3 m

Hence the correct choice is (c).

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