To develop this problem we will apply the concepts related to angular kinematic movement, related to linear kinematic movement. Linear velocity can be described in terms of angular velocity as shown below,

Here,
v = Lineal velocity
= Angular velocity
r = Radius
Our values are


Replacing to find the angular velocity we have,


Convert the units to RPM we have that


Therefore the angular speed of the wheels when the scooter is moving forward at 6.00 m/s is 955.41rpm
Answer:
The x-component and y-component of the velocity of the cruise ship relative to the patrol boat is -5.29 m/s and 0.18 m/s.
Explanation:
Given that,
Velocity of ship = 2.00 m/s due south
Velocity of boat = 5.60 m/s due north
Angle = 19.0°
We need to calculate the component
The velocity of the ship in term x and y coordinate


The velocity of the boat in term x and y coordinate
For x component,

Put the value into the formula


For y component,

Put the value into the formula


We need to calculate the x-component and y-component of the velocity of the cruise ship relative to the patrol boat
For x component,

Put the value into the formula


For y component,

Put the value into the formula


Hence, The x-component and y-component of the velocity of the cruise ship relative to the patrol boat is -5.29 m/s and 0.18 m/s.
Answer:
1. Energy = 2880 Joules.
2. Energy = 60 Joules.
3. Quantity of charge = 120 Coulombs.
Explanation:
Given the following data;
1. Voltage = 12 Volts
Current = 0.5 Amps
Time, t = 8 mins to seconds = 8 * 60 = 480 seconds
To find the energy;
Power = current * voltage
Power = 12 * 0.5
Power = 6 Watts
Next, we find the energy transferred;
Energy = power * time
Energy = 6 * 480
Energy = 2880 Joules
2. Charge, Q = 4 coulombs
Potential difference, p.d = 15V
To find the total energy transferred;
Energy = Q * p.d
Energy = 4 * 15
Energy = 60 Joules
3. Voltage = 6 Volts
Current = 1 Amps
Time = 2 minutes to seconds = 2 * 60 = 120 seconds
To find the quantity of charge;
Quantity of charge = current * time
Quantity of charge = 1 * 120
Quantity of charge = 120 Coulombs
The feather's vertical position
is determined by

We take the feather's starting position to be the origin, and the downward direction to be positive. Then

so the answer is D.