Answer:
22.02 m
Explanation:
given,
Force, F = 107 N
angle made with horizontal = 13.5◦
Power develop by the lawn roller = 69.4 W
time = 33 s
distance = ?
Force along horizontal= F cos θ
= 107 cos 13.5°= 104 N
Power = 
69.4 = 
W = 2290.2 J
Work done= Force x displacement
displacement= 
= 22.02 m
<h2>
Answer: 26,8 s</h2>
Explanation:
If we are talking about an acceleration at a constant rate , we are dealing with constant acceleration, hence we can use the following equations:
(1)
(2)
Where:
is the final velocity of the plane (the takeoff velocity in this case)
is the initial velocity of the plane (we know it is zero because it starts from rest)
is the constant acceleration of the plane to reach the takeoff velocity
is the distance of the runway
is the time
Knowing this, let's begin with (1):
(3)
(4)
(5)
Substituting (5) in (2):
(6)
Finding
:
This is the time needed to take off
Answer:
a. 0.143 mm b. 77.6 rad/m c. 483.18 rad/s d. +1
Explanation:
a. ym
Since the amplitude is 0.143 mm, ym = amplitude = 0.143 mm
b. k
We know k = wave number = 2π/λ where λ = wavelength.
Also, λ = v/f where v = speed of wave in string = √(T/μ) where T = tension in string = 19.3 N and μ = mass per unit length = 5.12 g/cm = 5.12 ÷ 1000 kg/(1 ÷ 100 m) = 0.512 kg/m and f = frequency = 76.9 Hz.
So, λ = v/f = √(T/μ)/f
substituting the values of the variables into the equation, we have
λ = √(T/μ)/f
= √(19.6 N/0.512 kg/m)/76.9 Hz
= √(38.28 Nkg/m)/76.9 Hz
= 6.187 m/s ÷ 76.9 Hz
= 0.081 m
= 81 mm
So, k = 2π/λ
= 2π/0.081 m
= 77.6 rad/m
c. ω
ω = angular frequency = 2πf where f = frequency of wave = 76.9 Hz
So, ω = 2πf
= 2π × 76.9 Hz
= 483.18 rad/s
d. The correct choice of sign in front of ω?
Since the wave is travelling in the negative x - direction, the sign in front of ω is positive. That is +1.
Answer:42.43m/s
Explanation:According to vf=vi+at, we can calculate it since v0 equals to 0. vf=0+9.8m/s^2*4.33s= 42.434m/s