A diverging lens has a focal length of 18.6 cm.
1 answer:
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The minimum height h is 65m so that the car will not fall off the track at the top of the circular part of the loop.
<h3>What is mechanical energy?</h3>Potential energy plus kinetic energy are combined to form mechanical energy. According to the principle of mechanical energy conservation, mechanical energy is constant in an isolated system when only conservative forces are acting on it. Potential energy increases when an object moves in the opposite direction of a conservative net force. Kinetic energy also changes as an object's speed, not velocity, changes. However, nonconservative forces, such as frictional forces, will always be present in real systems; however, if these forces are of minimal magnitude, mechanical energy changes little, making the idea of its conservation a reasonable approximation.
For completing the vertical circle the minimum speed at the bottom must be
so conserving mechanical energy
⇒ h=
h = 65m
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Answer:
x = 41.28 m
Explanation:
This is a projectile launching exercise, let's find the time it takes to get to the base of the cliff.
Let's start by using trigonometry to find the initial velocity
cos 25 = v₀ₓ / v₀
sin 25 = Iv_{oy} / v₀
v₀ₓ = v₀ cos 25
v_{oy} = v₀ sin 25
v₀ₓ = 22 cos 25 = 19.94 m / s
v_{oy} = 22 sin 25 = 0.0192 m / s
let's use movement on the vertical axis
y = y₀ + v_{oy} t - ½ g t²
when reaching the base of the cliff y = 0 and the initial height is y₀ = 21 m
0 = 21 + 0.0192 t - ½ 9.81 t²
4.905 t² - 0.0192 t - 21 = 0
t² - 0.003914 t - 4.2813 =0
we solve the quadratic equation
t =
t =
t₁ = 2.07 s
t₂ = -2.067 s
since time must be a positive scalar quantity, the correct result is
t = 2.07 s
now we can look up the distance traveled
x = v₀ₓ t
x = 19.94 2.07
x = 41.28 m