Aregulation basketball has a 22 cm di-
ameter and may be approximated as a thin
spherical shell.
how long will it take a basketball starting
from rest to roll without slipping 1.1 m down
an incline that makes an angle of 49.0° with
the horizontal? the acceleration of gravity is
9.81 m/s2.
answer in units of s.

0.70 s

Explanation:

Potential energy = kinetic energy + rotational energy

mgh = ½ mv² + ½ Iω²

For a thin spherical shell, I = ⅔ mr².

mgh = ½ mv² + ½ (⅔ mr²) ω²

mgh = ½ mv² + ⅓ mr²ω²

For rolling without slipping, v = ωr.

mgh = ½ mv² + ⅓ mv²

mgh = ⅚ mv²

gh = ⅚ v²

v = √(1.2gh)

v = √(1.2 × 9.81 m/s² × 1.1 m sin 49.0°)

v = 3.13 m/s

The acceleration down the incline is constant, so given:

Δx = 1.1 m

v₀ = 0 m/s

v = 3.13 m/s

Find: t

Δx = ½ (v + v₀) t

t = 2Δx / (v + v₀)

t = 2 (1.1 m) / (3.13 m/s + 0 m/s)

t = 0.704 s

Rounding to two significant figures, it takes 0.70 seconds.

kinetic

i'm so sorry if this is wrong i'm only in 6th grade xd

multiple allele inheritance is traits controlled by more than 2 alleles (ex: pigeons having 3 alleles of one gene govern their feather color).