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:

Explanation:
To solve this problem we use the formula for accelerated motion:

We will take the initial position as our reference (
) and the downward direction as positive. Since the rock departs from rest we have:

Which means our acceleration would be:

Using our values:

Answer:
The new height the ball will reach = (1/4) of the initial height it reached.
Explanation:
The energy stored in any spring material is given as (1/2)kx²
This energy is converted to potential energy, mgH, of the ball at its maximum height.
If the initial height reached is H
And the initial compression of the spring = x
So, mgH = (1/2)kx²
H = kx²/2mg
The new compression, x₁ = x/2
New energy of loaded spring = (1/2)kx₁²
And the new potential energy = mgH₁
mgH₁ = (1/2)kx₁²
But x₁ = x/2
mgH₁ = (1/2)k(x/2)² = kx²/8
H₁ = kx²/8mg = H/4 (provided all the other parameters stay constant)
The distance you free-fall from rest is D = (1/2) (g) (T²) <== memorize this
Height of the platform = (1/2) (9.8 m/s²) (2.4 sec)²
Height = (4.9 m/s²) (5.76 s²)
Height = (4.9/5.76) meters
Height = 28.2 meters (a VERY high platform ... about 93 ft off the water !)
Without air-resistance, your horizontal speed doesn't change. It's constant. Traveling 3.1 m/s for 2.4 sec, you cover (3.1 m/s x 2/4 s) = 7.4 m horizontally.