Answer:
about 19.6° and 73.2°
Explanation:
The equation for ballistic motion in Cartesian coordinates for some launch angle α can be written ...
y = -4.9(x/s·sec(α))² +x·tan(α)
where s is the launch speed in meters per second.
We want y=2.44 for x=50, so this resolves to a quadratic equation in tan(α):
-13.6111·tan(α)² +50·tan(α) -16.0511 = 0
This has solutions ...
tan(α) = 0.355408 or 3.31806
The corresponding angles are ...
α = 19.5656° or 73.2282°
The elevation angle must lie between 19.6° and 73.2° for the ball to score a goal.
_____
I find it convenient to use a graphing calculator to find solutions for problems of this sort. In the attachment, we have used x as the angle in degrees, and written the function so that x-intercepts are the solutions.
Answer:
Filters
Explanation:
Filters are transparent or translucent slices of glass or gelatin that are attached in front of the lens of cameras. Filters serve several purposes such as protecting the lens, regulating the amount of light that enters the film, thereby controlling exposure, as well as adding special effects to the images produced.
There are different types of filters that have their unique roles. Examples are the soft focus filter, neutral density filter, polarizing filter, and color balancing filter.
The answer is false! Hope that helps! :)
Answer:
It would take the object 5.4 s to reach the ground.
Explanation:
Hi there!
The equation of the height of a free-falling object at any given time, neglecting air resistance, is the following:
h = h0 + v0 · t + 1/2 · g · t²
Where:
h = height of the object at time t.
h0 = initial height.
v0 = initial velocity.
g = acceleration due to gravity (-32.2 ft/s² considering the upward direction as positive).
t = time
Let´s supose that the object is dropped and not thrown so that v0 = 0. Then:
h = h0 + 1/2 · g · t²
We have to find the time at which h = 0:
0 = 470 ft - 1/2 · 32.2 ft/s² · t²
Solving for t:
-470 ft = -16.1 ft/s² · t²
-470 ft / -16.1 ft/s² = t²
t = 5.4 s
The answer is C. 186. 6 g
The molar mass (Mr) of Mg(OH)₂ is the sum of atomic masses (Ar) of the elements.
Ar(Mg) = 24.3 g/mol
Ar(H) = 1
Ar(O) = 16
Mr(Mg(OH)₂) = Ar(Mg) + 2Ar(O) + 2Ar(H) = 24.3 + 2· 1 + 2 · *16 = 24.3 + 2 + 32 = 58.3 g/mol
Now, make a proportion. If 58.3 g are in 1 mol, how much will be in 3.2 mol:
58.3 g : 1 mol = x : 3.2 mol
x = 58.3 g · 3.2 mol ÷ 1 mol = 186.56 ≈ 186.6 g