Answer:
36.5°
Explanation:
Momentum is conserved immediately before and after the collision.
mâ uâ + mâ uâ = mâ vâ + mâ vâ
(0.020 kg) (100 m/s) + (1 kg) (0 m/s) = (0.020 kg) v + (1 kg) v
v = 1.96 m/s
After the collision, energy is conserved.
KE = PE
½ m v² = mgh
½ v² = gh
h = v² / (2g)
h = (1.96 m/s)² / (2 à 9.8 m/s²)
h = 0.196 m
We need the angle that the string forms with the vertical. Â Knowing the length of the string and the height that the block rises, we can do some geometry (see attached diagram).
L â L cos θ = h
L (1 â cos θ) = h
1 â cos θ = h / L
cos θ = 1 â h / L
cos θ = 1 â (0.196 m / 1 m)
θ = 36.5°
Round as needed.