140 Jules. Is the correct answer
Answer:
a) # lap = 301.59 rad
, b) L = 90.48 m
Explanation:
a) Let's use a direct proportions rule (rule of three). If one turn of the wire covers 0.05 cm, how many turns do you need to cover 24 cm
# turns = 1 turn (24 cm / 0.5 cm)
# laps = 48 laps
Let's reduce to radians
# laps = 48 laps (2 round / 1 round)
# lap = 301.59 rad
b) Each lap gives a length equal to the length of the circle
L₀ = 2π R
L = # turns L₀
L = # turns 2π R
L = 48 2π 30
L = 9047.79 cm
L = 90.48 m
A) We differentiate the expression for velocity to obtain an expression for acceleration:
v(t) = 1 - sin(2πt)
dv/dt = -2πcos(2πt)
a = -2πcos(2πt)
b) Any value of t can be plugged in as long as it is greater than or equal to 0.
c) we integrate the expression of velocity to find an expression for displacement:
∫v(t) dt = ∫ 1 - sin(2πt) dt
x(t) = t + cos(2πt)/2π + c
x(0) = 0
0 = = + cos(0)/2π + c
c = -1/2π
x(t) = t + cos(2πt)/2π -1/2π
Answer:
The rock's final speed at the required altitude will be 42.24 m/s.
Explanation:
Let's start by finding the initial vertical speed.
Vertical Speed = 1.61 * Sin (53.2°)
Vertical Speed = 0.8 m/s
We want to know the speed of the rock when it is at an altitude of 91 km.
The total displacement of the rock from its starting position will thus be equal to -91 km
We can use this in the following equation:
t = 4.3918 seconds
Thus it takes 4.3918 seconds to reach the required altitude. We can now find the speed as follows:
Thus the rock's final speed at the required altitude will be 42.24 m/s.
Answer:
λ = 28,14 m
Explanation:
To find the wavelength of the wave you use the following formula:
(1)
v: speed of the wave = 1,97 m/s
λ: wavelength
f: frequency of the wave = 0,07 Hz
You replace the values of v and f in the equation (1) and solve for λ:
hence, the wavelength of the wave is 28,14 m