Answer:
a. Acceleration, a = 1.88 m/s²
b. Time, t = 7.87 seconds.
Explanation:
Given the following data;
Initial velocity, U = 14.5m/s
Final velocity, V = 29.3m/s
Distance, S = 172m
a. To find the acceleration of the speedboat;
We would use the third equation of motion;
V² = U² + 2aS
Substituting into the formula
29.3² = 14.5² + 2a*172
858.49 = 210.25 + 344a
344a = 858.49 - 210.25
344a = 648.24
a = 648.24/344
Acceleration, a = 1.88 m/s²
b. To find the time;
We would use the first equation of motion;
V = U + at
29.3 = 14.5 + 1.88t
1.88t = 29.3 - 14.5
1.88t = 14.8
Time, t = 14.8/1.88
Time, t = 7.87 seconds.
Answer:

Explanation:
The magnitude of the net force exerted on q is known, we have the values and positions for
and q. So, making use of coulomb's law, we can calculate the magnitude of the force exerted by
on q. Then we can know the magnitude of the force exerted by
about q, finally this will allow us to know the magnitude of 
exerts a force on q in +y direction, and
exerts a force on q in -y direction.

The net force on q is:

Rewriting for
:

Answer:
Radio waves
Explanation:
The electromagnetic spectrum includes all different types of waves, which are usually classified depending on their frequency. Ordering them from the highest frequency to the lowest frequency, they are:
- Gamma rays
- X-rays
- Ultraviolet
- Visible light
- Infrared radiation
- Microwaves
- Radio waves
Radio waves are the electromagnetic waves with lowest frequency, their frequency is lower than 300 GHz (
) and therefore they are the electromagnetic waves with lowest energy (in fact, the energy of an electromagnetic wave is proportional to its frequency). They are generally used for radio and telecommunications since this type of waves can travel up to long distances.
Answer:
i. The radius 'r' of the electron's path is 4.23 ×
m.
ii. The frequency 'f' of the motion is 455.44 KHz.
Explanation:
The radius 'r' of the electron's path is called a gyroradius. Gyroradius is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field.
r = 
Where: B is the strength magnetic field, q is the charge, v is its velocity and m is the mass of the particle.
From the question, B = 1.63 ×
T, v = 121 m/s, Θ =
(since it enters perpendicularly to the field), q = e = 1.6 ×
C and m = 9.11 ×
Kg.
Thus,
r =
÷ sinΘ
But, sinΘ = sin
= 1.
So that;
r = 
= (9.11 ×
× 121) ÷ (1.6 ×
× 1.63 ×
)
= 1.10231 ×
÷ 2.608 × 
= 4.2266 ×
= 4.23 ×
m
The radius 'r' of the electron's path is 4.23 ×
m.
B. The frequency 'f' of the motion is called cyclotron frequency;
f = 
= (1.6 ×
× 1.63 ×
) ÷ (2 ×
× 9.11 ×
)
= 2.608 ×
÷ 5.7263 × 
= 455442.4323
f = 455.44 KHz
The frequency 'f' of the motion is 455.44 KHz.
Answer:
f = 1 m
Explanation:
The magnification of the lens is given by the formula:

where,
M = Magnification = 4
q = image distance = 5 m
p = object distance = ?
Therefore,

Now using thin lens formula:

<u>f = 1 m</u>