Help with the two questions above? Correct answers?
1 answer:
(6) first choice: the frequency appears higher and wavelength is shorter.
The car approaches a stationary observer and so the sound will appear to have shorter wavelength. This creates an effect of its siren to sound with higher frequency than it would do if both were stationary.
(7) The Doppler formula for frequency in the case of a stationary observer and source approaching it is as follows:
The wavelength is then
The third choice "0.80m; 431Hz" is correct
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Answer:
The plane is 2353.7 mi from the starting position.
Explanation:
Please, see the attached figure for a graphic representation of the problem.
We have 2 displacement vectors "a" and "b" and a vector "c" that is the sum of vectors "a" plus "b" (c = a + b). The module of "c" will be the distance of the plane from the starting point.
vector a = (xa, ya)
vector b = (xb, yb)
where “xa” and “xb” are the horizontal components of the vectors “a” and “b” respectively and “ya” and “yb” are the vertical components of each vector.
Then, the vector c = a + b will be:
c = (xa + xb, ya + yb)
The module of a vector is calculated using the following expression for a vector “v”:
module of v =
Then, the module of c will be:
module of c = = distance from starting point
Then, we have to find the components of vectors “a” and “b”
The distance traveled during the first 1.5 hours of the trip is the module of the vector “a”. Then:
module of a = = distance traveled during the first 1.5 hours.
The distance can be calculated using the equation of the position of an object moving in a straight line at constant speed:
x = x0 + v * t
where
x = position at time t
x0 = initial position
v = speed
t = time
Considering x0 as the starting point (x0 = 0)
x = 675 mi/h * 1.5 h = 1012.5 mi
Then:
module of a = = 1012. 5 mi
Since the plane moves only on the horizontal (see figure), the "y" component of the vector, "ya", will be 0.
Then:
(1012.5 mi)² = xa²
xa = 1012. 5mi
a = (1012.5 mi, 0)
In the same way, we have fo find the components of the vector “b”. The module of “b” will be the distance traveled during this part of the flight:
module of b = = x = x0 + v * t
Considering x0 as the point at which the plane turns (x0 = 0)
x = 675 mi / h * 2 h = 1350 mi
Using trigonometry, we can calculate xb and yb (see figure):
sin angle = opposite / hypotenuse
cos angle = adjacent / hypotenuse
In this case:
opposite = yb
adjacent = xb
hypotenuse = module of “b”
Then:
sin 10° = yb / module of “b”
sin 10° * module of “b” = yb
In the same way:
cos 10° * module of “b” = xb
Since module of “b” = 1350 mi
xb = 1329.5 mi
yb = 234.4 mi
b = (1329.5 mi, 234.4 mi)
The vector c = a+b can now be calculated:
c = (xa + xb, ya + yb)
c =(1012.5 mi + 1329.5 mi, 0 mi + 234.4 mi) = (2342 mi, 234.4 mi)
The module of c will be:
module of c = = 2353.7 mi
The plane is 2353.7 mi from the starting position.
The force needed to accelerate an elevator upward at a rate of is 2000 N or 2 kN.
<u>Explanation: </u>
As per Newton's second law of motion, an object's acceleration is directly proportional to the external unbalanced force acting on it and inversely proportional to the mass of the object.
As the object given here is an elevator with mass 1000 kg and the acceleration is given as , the force needed to accelerate it can be obtained by taking the product of mass and acceleration.
So 2000 N or 2 kN amount of force is needed to accelerate the elevator upward at a rate of .