Answer:
The final speed is 4.85 m/s.
Explanation:
Given:
Mass of ice (m) = 2.50 kg
Length of incline (L) = 2.00 m
Angle of incline (x) = 36.9°
Initial speed of ice block (u) = 0 m/s
Final speed of ice block (v) = ?
Friction is ignored.
So, when friction is ignored, then, the change in kinetic energy equals change in potential energy. This is true from conservation of energy.
∴ Δ KE = Δ PE
[tex]\frac{1}{2}m(v-u)^2=mg(h-0)\\\\v^2=2gh\\\\v=\sqrt{2gh}[/tex]
Here, 'h' is the initial height of the block which can be determined from the right angled triangle as shown below.
From triangle ABC, AC = 2.00 m, ∠ACB = 36.9°, AB = 'h'
So, using sine of angle ratio, we have
[tex]\sin (\angle ACB)=\frac{AB}{AC}\\\\h=\sin(36.9)\times 2.00=1.2\ m[/tex]
Therefore, the final speed is given as:
[tex]v=\sqrt{2\times 9.8\times 1.2}\\\\v=\sqrt{23.52}=4.85\ m/s[/tex]
Therefore, the final speed is 4.85 m/s.
