Answer:
Vi = 94.64 m/s
Explanation:
I order to find out the initial velocity of the object, we can use third equation of motion:
2ah = Vf² - Vi²
where,
a = acceleration = -9.8 m/s²
h = maximum height covered by object = 460 m - 3 m = 457 m
Vf = Final Velocity = 0 m/s (since, object momentarily stops at highest point)
Vi = Initial Velocity = ?
Therefore,
2(-9.8 m/s²)(457 m) = (0 m/s)² - Vi²
Vi = √8957.2 m²/s²
<u>Vi = 94.64 m/s</u>
Answer:
(a) 2.5 m/s
(b) 37.5 KJ
Explanation:
(a)
From the law of conservation of momentum, Initial momentum=Final momentum

and making
the subject then
and since
is initial velocity of car, value given as 4 m/s,
is the initial velocity of the three cars stuck together, value given as 2 m/s and
is the final velocity which is unknown. By substitution

(b)
Initial kinetic energy is given by

Final kinetic energy is given by

The energy lost is given by subtracting the final kinetic energy from the initial kinetic energy hence
Energy lost=350-312.5=37.5 KJ
Complete Question
A wave is described by y(x,t) = 0.1 sin(3x + 10t), where x is in meters, y is in centimetres and t is in seconds. The angular wave frequency is
Answer:
The value is 
Explanation:
From the question we are told that
The equation describing the wave is y(x,t) = 0.1 sin(3x + 10t)
Generally the sinusoidal equation representing the motion of a wave is mathematically represented as

Where w is the angular frequency
Now comparing this equation with that given we see that

Answer:
120 m
Explanation:
Given:
wavelength 'λ' = 2.4m
pulse width 'τ'= 100T ('T' is the time of one oscillation)
The below inequality express the range of distances to an object that radar can detect
τc/2 < x < Tc/2 ---->eq(1)
Where, τc/2 is the shortest distance
First we'll calculate Frequency 'f' in order to determine time of one oscillation 'T'
f = c/λ (c= speed of light i.e 3 x
m/s)
f= 3 x
/ 2.4
f=1.25 x
hz.
As, T= 1/f
time of one oscillation T= 1/1.25 x
T= 8 x
s
It was given that pulse width 'τ'= 100T
τ= 100 x 8 x
=> 800 x
s
From eq(1), we can conclude that the shortest distance to an object that this radar can detect:
= τc/2 => (800 x
x 3 x
)/2
=120m