Refer to the diagram shown below.
Given:
R = 6.37 x 10⁶ m, the radius of the earth
h = 3.58 x 10⁷ m, the height of the satellite above the earth's surface.
Therefore
R + h = 4.217 x 10⁷ m
In geosynchronous orbit, the period of rotation is 1 day.
Therefore the period is
T = (24 h)*(60 min/h)*(60 s/min) = 86400 s
The angular velocity is
ω = (2π rad)/(86400 s) = 7.2722 x 10⁻⁵ rad/s
Part (a)
The tangential speed is
v = (R+h)*ω
= (4.217 x 10⁷ m)*(7.2722 x 10⁻⁵ rad/s)
= 3066.7 m/s
= 3.067 km/s
Part (b)
The centripetal acceleration is
a = v²/(R+h)
= (3066.7 m/s)²/(4.217 x 10⁷ m)
= 0.223 m/s²
Answers:
(a) The speed is 3.067 km/s
(b) The acceleration is 0.223 m/s²
Answer:
<h3> b. 1.18</h3>
Explanation:
The fundamental frequency in string is expressed as;
F1 = 1/2L√T/m .... 1
L is the length of the string
T is the tension
m is the mass per unit length
If the tension is increased by 40%, the new tension will be;
T2 = T + 40%T
T2 = T + 0.4T
T2 = 1.4T
The new fundamental frequency will be;
F2 = 1/2L√1.4T/m ..... 2
Divide 1 by 2;
F2/F = (1/2L√1.4T/m)/1/2L√T/m)+
F2/F = √1.4T/m ÷ √T/m
F2/F = √1.4T/√m ×√m/√T
F2/F = √1.4T/√T
F2/F = 1.18√T/√T
F2/F = 1.18
F2 = 1.18F
Hence the fundamental frequency of vibration changes by a factor of 1.18
Answer:
Part a)

Part b)

Part c)

Explanation:
As we know that acceleration is rate of change in velocity of the object
So here we know that


Part a)
differentiate x and y two times with respect to time to find the acceleration






Now the acceleration of the object is given as

at t= 1.1 s we have

now the net force of the object is given as



now magnitude of the force will be

Part b)
Direction of the force is given as



Part c)
For velocity of the particle we have




now at t = 1.1 s

now the direction of the velocity is given as



Let s = rate of rotation
<span>Let r = radius of earth = 6,400km </span>
<span>Then solving (s^2) r = g will give the desired rate, from which length of day is inferred. </span>
<span>People would not be thrown off. They would simply move eastward in a straight line while the curved surface of earth fell away from beneath them.</span>