PLEASE PROVIDE EXPLANATION FOR D AND E

THANK YOU!

d) 14.1 m

e) 8.57 m/s

Explanation:

(a) There are three forces on the ball:

Normal force Fn pushing up,

Weight force Fg pulling down,

Kinetic friction Fk pushing left (resisting motion).

FBD is the correct free body diagram.

(b) Sum of forces in the y direction:

∑F = ma

Fn − Fg = 0

Fn = Fg

Sum of forces in the x direction:

∑F = ma

-Fk = ma

-Fn μk = ma

-mg μk = ma

a = -g μk

a = -(10 m/s²) (0.25)

a = -2.5 m/s²

(c) Sum of torques about the ball's center:

∑τ = Iα

Fk r = ⅖ mr² α

mg μk r = ⅖ mr² α

g μk = ⅖ r α

α = 5g μk / (2r)

α = 5 (10 m/s²) (0.25) / (2 × 0.2 m)

α = 31.25 rad/s²

(d) The velocity and angular velocity at time t is:

v = at + v₀

v = -2.5t + 12.0

ω = αt + ω₀

ω = 31.25t + 0

When the ball begins to roll without slipping, v = ωr.

-2.5t + 12.0 = (31.25t) (0.2)

-2.5t + 12.0 = 6.25t

12.0 = 8.75t

t = 1.37

The distance the ball moves is:

Δx = v₀ t + ½ at²

Δx = (12) (1.37) + ½ (-2.5) (1.37)²

Δx = 14.1 m

(e) v = at + v₀

v = (-2.5 m/s²) (1.37 s) + 12.0 m/s

v = 8.57 m/s

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.