I'm not quite sure what happens to Fay so I didn't finish but hope it helps
How do its eight arms help an octopus obtain food
1 answer:
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Answer:
The total linear acceleration is approximately 0.246 meters per square second.
Explanation:
The total linear acceleration () consist in two components, <em>radial</em> (
) and <em>tangential</em> (
), in meters per square second:
(1)
(2)
Since both components are orthogonal to each other, the total linear acceleration is determined by Pythagorean Theorem:
(3)
Where:
- Radius of the wheel, in meters.
- Angular speed, in radians per second.
- Angular acceleration, in radians per square second.
Given that wheel accelerates uniformly, we use the following kinematic equation:
(4)
Where:
- Initial angular speed, in radians per second.
- Time, in seconds.
If we know that ,
,
and
, then the total linear acceleration is:
The total linear acceleration is approximately 0.246 meters per square second.
Answer:
a) v₀ = 32.64 m / s , b) x = 59.68 m
Explanation:
a) This is a projectile launching exercise, we the distance and height of the cliff
x = v₀ₓ t
y = t - ½ g t²
We look for the components of speed with trigonometry
sin 43 = v_{oy} / v₀
cos 43 = v₀ₓ / v₀
v_{oy} = v₀ sin 43
v₀ₓ = v₀ cos 43
Let's look for time in the first equation and substitute in the second
t = x / v₀ cos 43
y = v₀ sin 43 (x / v₀ cos 43) - ½ g (x / v₀ cos 43)²
y = x tan 43 - ½ g x² / v₀² cos² 43
1 / v₀² = (x tan 43 - y) 2 cos² 43 / g x²
v₀² = g x² / [(x tan 43 –y) 2 cos² 43]
Let's calculate
v₀² = 9.8 60 2 / [(60 tan 43 - 25) 2 cos 43]
v₀ = √ (35280 / 33.11)
v₀ = 32.64 m / s
.b) we use the vertical distance equation with the speed found
y = t - ½ g t²
.y = v₀ sin43 t - ½ g t²
25 = 32.64 sin 43 t - ½ 9.8 t²
4.9 t² - 22.26 t + 25 = 0
t² - 4.54 t + 5.10 = 0
We solve the second degree equation
t = (4.54 ±√(4.54 2 - 4 5.1)) / 2
t = (4.54 ± 0.46) / 2
t₁ = 2.50 s
t₂ = 2.04 s
The shortest time is when the cliff passes and the longest when it reaches the floor, with this time we look for the horizontal distance traveled
x = v₀ₓ t
x = v₀ cos 43 t
x = 32.64 cos 43 2.50
x = 59.68 m