Answer:
(a) the angular velocity at θ1 is 11.64 rad/s
(b) the angular acceleration is 0.12 rad/
(c) the angular position was the disk initially at rest is - 428.27 rad
Explanation:
Given information :
θ1 = 16 rad
θ2 = 76 rad
ω2 = 11 rad/s
t = 5.3 s
(a) The angular velocity at θ1
First, we use the angular motion equation for constant acceleration
Δθ = (ω1+ω2)t/2
θ2 - θ1 = (ω1+ω2)t/2
ω1 + ω2 = 2 (θ2 - θ1) / t
ω1 = (2 (θ2 - θ1) / t ) - ω2
= (2 (76-16) / 5.3) - 11
= 11.64 rad/s
(b) the angular acceleration
ω2 = ω1 + α t
α t = ω2 - ω1
α = (ω2 - ω1)/t
= (11.64 - 11) / 5.3
= 0.12 rad/
(c) the angular position was the disk initially at rest, θ0
at rest ω0 = 0
ω2^2 = ω01 t + 2 α Δθ
2 α Δθ = ω2^2
θ2 - θ0 = ω2^2 / 2 α
θ0 = θ2 - (ω2^2) / 2 α
= 76 - (
/ 2 x 0.12
= 76 - 504.16
= - 428.27 rad
Answer:
49.07 miles
Explanation:
Angle between two ships = 110° = θ
First ship speed = 22 mph
Second ship speed = 34 mph
Distance covered by first ship after 1.2 hours = 22×1.2 = 26.4 miles = b
Distance covered by second ship after 1.2 hours = 34×1.2 = 40.8 miles = c
Here the angle between the two sides of a triangle is 110° so from the law of cosines we get
a² = b²+c²-2bc cosθ
⇒a² = 26.4²+40.8²-2×26.4×40.8 cos110
⇒a² = 2408.4
⇒a = 49.07 miles
Answer:
See the explanation below.
Explanation:
The force is a vector therefore we can decompose the force into components x & y. as we need the horizontal component of the force, we must use the cosine function of the angle.
![F_{1x}=30.8*cos(20)\\F_{1x}=28.94[N]\\F_{2x}=34.3*cos(20)\\\\F_{2x}= 32.23[N]](https://tex.z-dn.net/?f=F_%7B1x%7D%3D30.8%2Acos%2820%29%5C%5CF_%7B1x%7D%3D28.94%5BN%5D%5C%5CF_%7B2x%7D%3D34.3%2Acos%2820%29%5C%5C%5C%5CF_%7B2x%7D%3D%2032.23%5BN%5D)
Scott-Dannemiller, Koeninger, Briscoe, and Carter
Christopher-Briscoe, Dannemiller, and Koeninger
Dianne-Koeninger, Briscoe, and Carter
Kailee-Koeninger and Carter
