Question

# For a particle projected from an inclined plane as shown in the figure, choose the correct statement(s) regarding the projectile.

A
Time of flight of projectile is 3 s
B
Range of projectile (OP) is 803 m
C
Range of projectile (OP) is 802 m
D
Time of flight of projectile is 4 s

Solution

## The correct options are C Range of projectile (OP) is 80√2 m D Time of flight of projectile is 4 sTaking the X−axis along the inclined plane and Y−axis perpendicular to the inclined plane. Along Y−axis, uy=20sin45=20√2=10√2 m/s  ay=−gcos45=−10√2=−5√2 m/s2 sy=0 [Particle returns to inclined plane, hence displacement along Y-axis is zero] ⇒sy=uyt+12ayt2 ⇒0=10√2t−12×5√2×t2 ⇒t=10√2×25√2=4 s ∴T=4 s     ...(1) (Time of flight) Along X−axis, ux=20cos45∘=20×1√2=10√2 m/s ax=10sin45∘=10×1√2=5√2 m/s2 Range of the particle, sx=OP Applying   sx=uxt+12axt2 ⇒OP=10√2×4+12×5√2×16 ∴OP=40√2+40√2=80√2 m Time of flight of the projectile is 4 s and its range is 80√2 m.

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