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.
From the formula, V=displacement/time
displacement/distance =velocity*time
distance=1200*2.5
distance=3*10³km
<span>Bakers making fruit pies face the problem of the fruit juices running out into the oven and having a soggy crust. An ingenious way of preventing this is to put a paper cone made of thick brown paper in the hole at the center of the top
crust as you put the pie in the oven. When the fruit juice boils, it rises into this funnel and then goes back down into the pie, preventing the juice from overflowing all over the crust. Pinching together the upper and lower crusts will prevent the juice from seeping out from the edges.</span>
Work done is 0.442J
<u>Explanation:</u>
Given:
Spring constant, k = 33 N/m
Distance, x₁ = 0.15m
Additional distance, x₂ = 0.072 m
Total distance = 0.15 + 0.072 m
= 0.222 m
Work done, W = ?
We can calculate work done by the formula
On substituting the value we get:
![W = \frac{1}{2}k [(x_2)^2 - (x_1)^2]\\ \\W = \frac{1}{2} X 33[(0.222)^2 - (0.15)^2]\\ \\W = \frac{1}{2}X 33 [ 0.0493 - 0.0225]\\ \\W = 0.442 J](https://tex.z-dn.net/?f=W%20%3D%20%5Cfrac%7B1%7D%7B2%7Dk%20%5B%28x_2%29%5E2%20%20-%20%28x_1%29%5E2%5D%5C%5C%20%5C%5CW%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20X%2033%5B%280.222%29%5E2%20-%20%280.15%29%5E2%5D%5C%5C%20%5C%5CW%20%3D%20%5Cfrac%7B1%7D%7B2%7DX%2033%20%5B%200.0493%20-%200.0225%5D%5C%5C%20%5C%5CW%20%3D%200.442%20J)
Therefore, work done is 0.442J
Answer:
λ = 6.802 10⁻⁷ m, wavelength corresponds to orange almost red
Explanation:
The expression for constructive interference is
d sin θ = m λ
let's use trigonometry
tan θ = y / L
tan θ = sin θ / cos θ
interference experiments angles are very small
tan θ = sin θ = y / L
substituting
= m λ
in this case they indicate the separation of the slits d = 7.16 10-5 m, the order of the interference is m = 4, the distance y = 3.8 10-2 m and the separation to the screen L = 1 m
A) they ask us for the wavelength
λ = 
let's calculate
λ = 7.16 10⁻⁵ 3.8 10⁻² /(4 1)
λ = 6.802 10⁻⁷ m
B) Let's reduce the wavelength to nm
λ = 6.802 10⁻⁷ m (109 nm / 1m)
λ = 680.2 nm
this wavelength corresponds to orange almost red
