Problem 1.13 An airplane in level flight at an altitude h and a uniform speed v passes directly over a
radar tracking station A. Calculate the angular velocity
and angular acceleration
of the radar
antenna as well as the rate
&
r
at which the airplane is moving away from the antenna. Use the equations
of this chapter (rather than polar coordinates, which you can use to check your work). Attach the inertial
frame of reference to the ground and assume a non-rotating earth. Attach the moving frame to the
antenna, with the x axis pointing always from the antenna towards the airplane,
ˆ
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 1
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 1
Problem 1.14 At 30° north latitude, a 1000 kg (2205 lb) car travels due north at a constant speed of 100
km/h (62 mph) on a level road at sea level. Taking into account the earth’s rotation, calculate the lateral
(sideways) force of the road on the car and the normal force of the road on the car.
Solution
Problem 1.15 At 29° north latitude, what is the deviation d from the vertical of a plumb bob at the end
of a 30 m string, due to the earth’s rotation?
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 1
Problem 1.16 Verify by substitution that Equation 1.114a is the solution of Equation 1.113.
(3)
xce
dtBcos
dt
Then
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 1
Problem 1.17 Verify that Equation 1.114b is valid
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 1
Problem 1.18 Numerically solve the fourth-order differential equation
&&&&
y2&&
yy0
for y at t = 20, if
the initial conditions are
y1
,
&
y&&
y&&&
y0
at t = 0.