Answer:
4.1 seconds
Explanation:
The height of the football is given by the equation:
Using the inicial position S = 4 and the inicial velocity V = 64, we can find the time when the football hits the ground (H = 0):
Using Bhaskara's formula, we have:
A negative time is not a valid result for this problem, so the amount of time the football is in the air before hitting the ground is 4.1 seconds.
Considering the Doppler efect, the frequency heard by the student would change if:
- if the student walked toward the police car.
- if the student walked away from the police car.
- if the police car moved toward the student.
- if the police car moved away from the student.
<h3>Doppler effect</h3>
The Doppler effect is defined as the change in the apparent frequency of a wave produced by the relative motion of the source with respect to its observer. In other words, this effect is the change in the perceived frequency of any wave motion when the sender and receiver, or observer, move relative to each other.
The following expression is considered the general case of the Doppler effect:
Where:
- f', f: Frequency perceived by the receiver and frequency emitted by the transmitter, respectively. Its unit of measurement in the International System (S.I.) is the hertz (Hz), which is the inverse unit of the second (1 Hz = 1 s⁻¹)
- v: Wave propagation speed in the medium. It is constant and depends on the characteristics of the medium. In this case, the speed of sound in air is considered to be 343 m/s.
- vR, vE: Receiver and transmitter speed respectively. Its unit of measure in the S.I. is the m/s
- ±, ∓:
- We will use the + sign:
- In the numerator if the receiver approaches the sender
- In the denominator if the sender moves away from the receiver
- In the numerator if the receiver moves away from the sender
- In the denominator if the sender approaches the receiver
In summary, the Doppler Effect is an alteration of the observed frequency of a sound due to the movement of the source or the observer, that is, they are changes in the frequency and wavelength of a wave due to the relative movement between the wave source and the observer.
<h3>Changes on the frequency </h3>
In this case, considering the Doppler effect, the frequency heard by the student would change if:
- if the student walked toward the police car.
- if the student walked away from the police car.
- if the police car moved toward the student.
- if the police car moved away from the student.
Learn more about Doppler effect:
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Answer:
a) t = 3.027 10⁻⁹ s
, b) y = 2.25 10⁻² m
Explanation:
We can solve this problem using the kinematic relations
a) as on the x-axis there is no relationship
vₓ = x / t
t = x / vₓ
We reduce the magnitudes to the SI system
x = 5.6 cm (1m / 100 vm) = 0.056 m
we calculate
t = 0.056 / 1.85 10⁷
t = 3.027 10⁻⁹ s
b) the time is the same for the two movements, on the y axis
y = v₀t + ½ a t²
as the beam leaves horizontal there is no initial vertical velocity
y = ½ a t²
let's calculate
y = ½ 5.45 10¹⁵ (3.027 10⁻⁹)²
y = 2.25 10⁻² m
To solve this problem we use the general kinetic equations.
We need to know the time it takes for the car to reach 130 meters.
In this way we have to:
Where
= initial position
= initial velocity
= acceleration
= time
= position as a function of time
.
We use the quadratic formula to solve the equation.
t = 6.63 s and t = -17.1 s
We take the positive solution. This means that the car takes 6.63 s to reach 130 meters.
Then we use the following equation to find the final velocity:
Where:
= final speed
The final speed of the car is 27.25 m/s
