Answer:
Explanation:
Applying trigonometry to calculate the slope's height:
sinθ = opposite / hypotenuse
sin 4° = h / 100
h = 100 × sin 4°
h = 6.98 m
Using conservation of energy principles:
Change in potential energy equals change in kinetic energy,
∆PE = ∆KE
mg(hf - hi) = ½ m (vf² - vi²)
The initial speed is:
vi = 9.2 m/s
Initial height is:
hi = 6.98 m
Final height when the sled reaches the ground:
hf = 0 m
We solve for final velocity vf:
mg(hf - hi) = ½ m (vf² - vi²)
Mass cancels out:
g(hf - hi) = ½ (vf² - vi²)
9.81 × (0 - 6.98) = ½ (vf² - 9.2²)
-68.43 = ½ (vf² - 84.64)
Multiplying both sides by 2:
-136.86 = vf² - 84.64
vf² = -136.86 + 84.64 = -52.22 (This is inconsistent; correcting the sign)
Actually, hf - hi = 0 - 6.98 = -6.98, but since the sled is descending, potential energy loss is positive, so flip the signs:
g(hi - hf) = ½ (vf² - vi²)
9.81 × 6.98 = ½ (vf² - 9.2²)
68.43 = ½ (vf² - 84.64)
136.86 = vf² - 84.64
vf² = 136.86 + 84.64 = 221.5
vf = √221.5 = 14.88 m/s