<span>2π/T = 2π/10 = π/5
y(x) = A sin (wx) = 0.75 sin (πx/5)
y(4) = 0.75 sin (4π/5) = 0.4408389392... ≈ 0.441</span><span>
</span>
Answer:
4.17 m/s²
Explanation:
We are told the reaction time is 0.2 s. Now, during this reaction time the car is going to travel an additional distance of
: x = u × t = 40 × 0.2 = 8 m
where u is the initial velocity of the car which is 40.0 m/s.
We are told that he had 200 m to stop before applying brakes. Thus, after applying brakes, he now has a distance to cover of; s = 200 - 8 = 192 m
Since vehicle is coming to rest acceleration would be negative, thus using Newton's equation of motion, we have;
v
² = u² - 2as
v = 0 m/s since it's coming to rest
u = 40 m/s
s = 192 m
Thus;
0² = 40² - 2(a)(192)
0² = 1600 - 384a
a = 1600/384
a = 4.17 m/s²
Answer:
56 kg
Explanation:
The change in potential energy of the man is given by:
where
m is the man's mass
g is the gravitational acceleration
is the change in height of the man
In this problem, we have:
is the gain in potential energy
g = 9.8 m/s^2 is the gravitational acceleration
is the change in height
Re-arranging the equation and substituting the numbers, we find the mass:
By the law of momentum conservation:-
=>m¹u¹ + m²u² = m1v1 + m²v² {let East is +ve}
=>u¹ + u² = v¹ + v² {as m1=m2}
=>3.5 - 2.75 = v1-1.5
<span>
=>v¹ = 2.25 m/s (East) </span>
Answer:
The lowest possible frequency of sound for which this is possible is 1307.69 Hz
Explanation:
From the question, Abby is standing 5.00m in front of one of the speakers, perpendicular to the line joining the speakers.
First, we will determine his distance from the second speaker using the Pythagorean theorem
l₂ = √(2.00²+5.00²)
l₂ = √4+25
l₂ = √29
l₂ = 5.39 m
Hence, the path difference is
ΔL = l₂ - l₁
ΔL = 5.39 m - 5.00 m
ΔL = 0.39 m
From the formula for destructive interference
ΔL = (n+1/2)λ
where n is any integer and λ is the wavelength
n = 1 in this case, the lowest possible frequency corresponds to the largest wavelength, which corresponds to the smallest value of n.
Then,
0.39 = (1+ 1/2)λ
0.39 = (3/2)λ
0.39 = 1.5λ
∴ λ = 0.39/1.5
λ = 0.26 m
From
v = fλ
f = v/λ
f = 340 / 0.26
f = 1307.69 Hz
Hence, the lowest possible frequency of sound for which this is possible is 1307.69 Hz.