Answer:
The speed of the baseball is approximately 19.855 m/s
Explanation:
From the question, we have;
The frequency of the microwave beam emitted by the speed gun, f = 2.41 × 10¹⁰ Hz
The change in the frequency of the returning wave, Δf = +3190 Hz higher
The Doppler shift for the microwave frequency emitted by the speed gun which is then reflected back to the gun by the moving baseball is given by 2 shifts as follows;


Where;
Δf = The change in frequency observed, known as the beat frequency = 3190 Hz
= The speed of the baseball
c = The speed of light = 3.0 × 10⁸ m/s
f = The frequency of the microwave beam = 2.41 × 10¹⁰ Hz
By plugging in the values, we have;


The speed of the baseball,
≈ 19.855 m/s
Answer:
3.9 m/s
Explanation:
We are given that
Mass of car,m=
Initial velocity,u=0
Distance,s=5.9 m

Average friction force,f=
We have to find the speed of the car at the bottom of the driveway.
Net force,
Where 
Acceleration,


v=3.9 m/s
<span>The mechanical energy is conserved.
I hope this helps, good luck! :)</span>
Answer:
She can swing 1.0 m high.
Explanation:
Hi there!
The mechanical energy of Jane (ME) can be calculated by adding her gravitational potential (PE) plus her kinetic energy (KE).
The kinetic energy is calculated as follows:
KE = 1/2 · m · v²
And the potential energy:
PE = m · g · h
Where:
m = mass of Jane.
v = velocity.
g = acceleration due to gravity (9.8 m/s²).
h = height.
Then:
ME = KE + PE
Initially, Jane is running on the surface on which we assume that the gravitational potential energy of Jane is zero (the height is zero). Then:
ME = KE + PE (PE = 0)
ME = KE
ME = 1/2 · m · (4.5 m/s)²
ME = m · 10.125 m²/s²
When Jane reaches the maximum height, its velocity is zero (all the kinetic energy was converted into potential energy). Then, the mechanical energy will be:
ME = KE + PE (KE = 0)
ME = PE
ME = m · 9.8 m/s² · h
Then, equallizing both expressions of ME and solving for h:
m · 10.125 m²/s² = m · 9.8 m/s² · h
10.125 m²/s² / 9.8 m/s² = h
h = 1.0 m
She can swing 1.0 m high (if we neglect dissipative forces such as air resistance).