40 km/h to in/s
60*60=3600 seconds in an hour
one km is about 0.621 miles
40 km is about 0.621*40=24.84 miles
5280 feet in a mile
12 inches on each foot
5280*12=63360 inches in a mile
63360*24.84=1573862.4 inches in 40km
40 km/h = 40*1573862.4/3600=17487.36 in/s
Answer:
a) The velocity of the car is 7.02 m/s and the car is approaching to the police car as the frequency of the police car is increasing.
b) The frequency is 1404.08 Hz
Explanation:
If the police car is a stationary source, the frequency is:
(eq. 1)
fs = frequency of police car = 1200 Hz
fa = frequency of moving car as listener
v = speed of sound of air
vc = speed of moving car
If the police car is a stationary observer, the frequency is:
(eq. 2)
Now,
fL = frequecy police car receives
fs = frequency police car as observer
a) The velocity of car is from eq. 2:
b) Substitute eq. 1 in eq. 2:
Answer:
Fx= 50.0 Pounds : Components of the force along the x-axis
Fy= 86.6 Pounds : Component of the force along the y-axis
Explanation:
Conceptual Analysis
To find the components (Fx, Fy) of the total force (F), we apply the trigonometric concepts for a right triangle, where the perpendicular sides of the triangle are the components (Fx, Fy) of the force (F), the hypotenuse (h) is the magnitude of the total force F and β is the angle that forms the horizontal component with the hypotenuse.
Formulas
cos β : x/h : x: side adjacent to the β angle h: hypotenuse (1)
sin β = y/h : y: side opposite to the β angle h: hypotenuse (2)
Known Data
Known data
F= 1.00 * 10² pounds = 100 pounds : magnitude of total force
β = 60.0° to the x-axis. : Angle that forms the force with the x-axis
Problem Development
We apply the formula 1 to calculate horizontal component (Fx)
cos β :Fx/F
Fx= F cosβ = 100*cos 60° = 50.0 Pounds
We apply the formula 2 to calculate vertical component (Fy)
sin β = Fy/F
Fy= F sinβ = 100*sin 60° = 86.6 Pounds
