A board is being moved with a cosntant velocity v 0 on a smooth horizontal plane. A small block is projected on the rough boards. Coefficient of friction between board and block is μ = 0.3 . Block i

Question

A board is being moved with a cosntant velocity $v_{0}$ on a smooth horizontal plane. A small block is projected on the rough boards. Coefficient of friction between board and block is $μ = 0.3$ . Block is projected with velocity $v_{1} = 25 m / s$ at an angle of $θ = 3 7^{\circ}$ relative to ground. What is the velocity of block (in $m / s$ ) relative to ground after time $t = 10 sec$ ?

TestHub · Accepted Answer

v b ​ = 8 i ^ m / s v 1 x ​ = 25 cos ( 3 7 ∘ ) = 25 × 0.8 = 20 m / s v 1 y ​ = 25 sin ( 3 7 ∘ ) = 25 × 0.6 = 15 m / s v 1 ​ = ( 20 i ^ + 15 j ^ ​ ) m / s v re l ​ = v 1 ​ − v b ​ = ( 20 − 8 ) i ^ + 15 j ^ ​ = 12 i ^ + 15 j ^ ​ v re l ​ = 1 2 2 + 1 5 2 ​ = 144 + 225 ​ = 369 ​ ≈ 19.21 m / s a = μg = 0.3 × 10 = 3 m / s 2 t 0 ​ = a v re l ​ ​ = 3 369 ​ ​ ≈ 6.4 s v f ina l ​ = v b ​ = 8 i ^ m / s Magnitude: 8 m / s

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JEE Main 2027 (Class 12+)