Answer:
1.024 × 10⁸ m
Explanation:
The velocity v₀ of the orbit 8RE is v₀ = 8REω where ω = angular speed.
So, ω = v₀/8RE
For the orbit with radius R for it to maintain a circular orbit and velocity 2v₀, we have
2v₀ = Rω
substituting ω = v₀/8RE into the equation, we have
2v₀ = v₀R/8RE
dividing both sides by v₀, we have
2v₀/v₀ = R/8RE
2 = R/8RE
So, R = 2 × 8RE
R = 16RE
substituting RE = 6.4 × 10⁶ m
R = 16RE
= 16 × 6.4 × 10⁶ m
= 102.4 × 10⁶ m
= 1.024 × 10⁸ m
Answer:
2.39 revolutions
Explanation:
As she jumps off the platform horizontally at a speed of 10m/s, the gravity is the only thing that affects her motion vertically. Let g = 10m/s2, the time it takes for her to fall 10m to water is
Knowing the time it takes to fall to the pool, we calculate the angular distance that she would make at a constant acceleration of 15 rad/s2:
As each revolution is 2π, the total number of revolution that she could make is: 15 / 2π = 2.39 rev
Centripetal acceleration = (speed)² / (radius) .
Force = (mass) · (acceleration)
Centripetal force = (mass) · (speed)² / (radius) .
= (11 kg) · (3.5 m/s)² / (0.6 m)
= (11 kg) · (12.25 m²/s²) / (0.6 m)
= (11 · 12.25) / 0.6 kg-m/s²
= 224.58 newtons. (about 50.5 pounds)
That's the tension in Miguel's arm or leg or whatever part of his body
Jesse is swinging him by. It's the centripetal force that's needed in
order to swing 11 kg in a circle with a radius of 0.6 meter, at 3.5
meters/second. If the force is less than that, then the mass has to
either swing slower or else move out to follow a bigger circle.
<span>θ=0.3sin(4t)
w=0.3cost(4t)(4)=1.2cost(4t)
a=-4.8sin(4t)
cos4t max will always be 1 (refer to cos graph), for same reason, sin4t will always be 0
therefore, wmax=1.2rad/s
vAmax=r*w=250*1.2=300mm/s
(may be different if your picture/radius is from a different picture)
adt=a*r=200*-4.8sin(4t)=0 (sin(4t)=0)
adn=r*w^2=200*1.2^2=288
ad= square root of adt^2+adn^2 = 288mm/s^2</span>
