Answer:
y = 67.6 feet, y = 114.4/ (22 - 3t)
Explanation:
For this exercise let's use that light travels in a straight line and some trigonometric relationships, the symbols are in the attached diagram
Large triangle Projector up to the screen
tan θ = y / L
For the small triangle. Projector up to the person
tan θ = y₀ / (L-d)
The angle is the same, so we equate the two equations
y₀ / (L -d) = y / L
y = y₀ L / (L-d)
The distance from the screen (d), we look for it with kinematics
v = d / t
d = v t
we replace
y = y₀ L / (L - v t)
y = 5.2 22 / (22 - 3 t)
y = 114.4 (22 - 3t)⁻¹
This is the equation of the shadow height change as a function of time
For the suggested distance the shadow has a height of
y = 114.4 / (22-13)
y = 67.6 feet
Answer:
(a) 17.37 rad/s^2
(b) 12479
Explanation:
t = 95 s, r = 6 cm = 0.06 m, v = 99 m/s, w0 = 0
w = v / r = 99 / 0.06 = 1650 rad/s
(a) Use first equation of motion for rotational motion
w = w0 + α t
1650 = 0 + α x 95
α = 17.37 rad/s^2
(b) Let θ be the angular displacement
Use third equation of motion for rotational motion
w^2 = w0^2 + 2 α θ
1650^2 = 0 + 2 x 17.37 x θ
θ = 78367.87 rad
number of revolutions, n = θ / 2 π
n = 78367.87 / ( 2 x 3.14)
n = 12478.9 ≈ 12479
Answer:
<em><u>Assuming that the vertical speed of the ball is 14 m/s</u></em> we found the given values:
a) V₀ = 23.4 m/s
b) h = 27.9 m
c) t = 0.96 s
d) t = 4.8 s
Explanation:
a) <u>Assuming that the vertical speed is 14 m/s</u> (founded in the book) the initial speed of the ball can be calculated as follows:

<u>Where:</u>
: is the final speed = 14 m/s
: is the initial speed =?
g: is the gravity = 9.81 m/s²
h: is the height = 18 m
b) The maximum height is:


c) The time can be found using the following equation:


d) The flight time is given by:

I hope it helps you!
1) 4min = 4*60 sec = 240 sec
2) Distance = speed times time = 3 * 240 = 720 m
Answer:
50.4°
Explanation:
Snell's law states:
n₁ sin θ₁ = n₂ sin θ₂
where n is the index of refraction and θ is the angle of incidence (relative to the normal).
When θ₁ = 48°:
n sin 48° = 1.33 sin 72°
n = 1.702
When θ₁ = 37°:
1.702 sin 37° = 1.33 sin θ
θ = 50.4°