The block accelerates down the ramp due to the component of its weight that acts parallel to the ramp; this force has magnitude
(100 kg) g sin(26.6°) ≈ 438 N
(Note that the positive sign here means we take "down the ramp" to be the positive direction.)
Since the ramp is frictionless, this is the only force acting on the block in this direction. By Newton's second law, the block's acceleration is a such that
438 N ≈ (100 kg) a ⇒ a ≈ 4.38 m/s²
The block accelerates uniformly, so that it attains a speed v as it moves 50 m such that
v² = 2a (50 m)
Solve for v :
v = √(2a (50 m)) ≈ 20.9 m/s
