1) The work performed on the spores is
2) The spores land 0.32 m away
Explanation:
1)
According to the work-energy principle, the work done on the spores equals their change in kinetic energy:
where
W is work done
m represents the spore's mass
v is the final velocity
u is the initial velocity
Given:
spore mass =
initial velocity u = 0 (starting from rest)
final velocity v = 7.0 m/s
Calculating the work:
2)
The spores follow projectile motion, moving along a parabolic trajectory made of two motions:
- Constant speed horizontally
- Vertically accelerated due to gravity
Considering vertical motion first, using kinematics:
where
s = 0.01 m (shooting height)
u = 0 (no initial vertical velocity, horizontal ejection)
t = time of flight
g = acceleration due to gravity
Solving for t:
Now for horizontal displacement, when velocity is constant:
where
horizontal velocity =
time t = 0.045 s
Calculating distance d:
Thus, the spores land 0.32 meters away.
Learn more about work:
Learn more about projectile motion:
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Answer:
The period of a wave is the duration it takes to complete one full oscillation, such as from one peak to the next trough.
Since the period is expressed in microseconds, it needs to be converted into seconds.
The conversion is:
Accordingly, the wave's period in seconds is .
Answer:
The total energy can be expressed as
Explanation:
The problem states that
The Poynting vector, which measures energy flux, equals
The rectangle's length is represented by
The width of the rectangle is
The duration considered is
Mathematically, the overall electromagnetic energy incident on the area is given by
where A denotes the area of the rectangle, calculated as
By plugging in the respective values
Again substituting values