Answer:
A lake full of a larger variety of fish, frogs, and birds
The distance d₁ it rises from rest while the engine is burning is given by
d₁ = d₀ + v₀t + (1/2)at²
d₁ = 0 + 0 + (1/2)·(29.4 m/s²)·(3.98 s)² = 232.85 m
So it gets to 232.85 m and then runs out of fuel. Its velocity v₁ at this point is given by
v₁ = v₀ + at = (29.4 m/s²)·(3.98 s) = 117 m/s
At this point, gravity begins to slow it down until it reaches its peak where its velocity v₂ is zero.
v₂² = v₁² + 2ad₂
where d₂ is the distance it rises until v=0
Since gravity is decelerating the rocket, a = -g, and we have
0² = (117 m/s)² + 2(-9.8 m/s²)d₂
0 = (117)² - (19.6)·d₂
0 = 13,689 - (19.6)·d₂
d₂ = 13,689/19.6 = 698.42 m
So the total height it rises is given by
d₁ + d₂ = 232.85 m + 698.42 m
= 931.27 m
Answer:
2.25m/s
Explanation:
wavelength=4.5m
period=2sec
frequency= 1/period
=1/2
speed= wavelength×wave frequency
=4.5×1/2
=2.25 m/s
so, none of the options are correct
Answer:
0.82052 m
Explanation:
potential energy of spring = kinetic energy
=> 0.5kx^2 = 0.5mv^2
=> 

v= 3.11127 m/s
angle = 37°
thus height = distance×sin(37) = D×0.60182
Also,
m×g×h = 0.5×m×v^2
=> 2×9.8×D×0.60182 = 0.5×2×3.11127×3.11127
=> D = 0.82052 m
The ducks' flight path as observed by someone standing on the ground is the sum of the wind velocity and the ducks' velocity relative to the wind:
ducks (relative to wind) + wind (relative to Earth) = ducks (relative to Earth)
or equivalently,

(see the attached graphic)
We have
- ducks (relative to wind) = 7.0 m/s in some direction <em>θ</em> relative to the positive horizontal direction, or

- wind (relative to Earth) = 5.0 m/s due East, or

- ducks (relative to earth) = some speed <em>v</em> due South, or

Then by setting components equal, we have


We only care about the direction for this question, which we get from the first equation:



or approximately 136º or 224º.
Only one of these directions must be correct. Choosing between them is a matter of picking the one that satisfies <em>both</em> equations. We want

which means <em>θ</em> must be between 180º and 360º (since angles in this range have negative sine).
So the ducks must fly (relative to the air) in a direction 224º relative to the positive horizontal direction, or about 44º South of West.