The launch velocity of the marble launcher is 34.65 m/s
Given that the launch velocity of marble launcher, launches a 25g marble to a distance of 73 cm (0.73 m) and the marble roll up to 6.2 meters before stopping. The launch height is 20 cm (0.2 m).
The time for landing can be calculated by the second equation of motion formula:
h = ut +
g
Let u = 0
0.2 = 0×t +
× 9.8 × 
= 
= 0.04
t = 0.2s
Now, the launch velocity of the marble launcher can be calculated by:
Speed = Distance / Time
Speed = 
Speed = 
Speed = 34.65 m/s
Therefore, the launch velocity of the marble launcher is 34.65 m/s
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Answer:
Approximately 21 km.
Explanation:
Refer to the not-to-scale diagram attached. The circle is the cross-section of the sphere that goes through the center C. Draw a line that connects the top of the building (point B) and the camera on the robot (point D.) Consider: at how many points might the line intersects the outer rim of this circle? There are three possible cases:
- No intersection: There's nothing that blocks the camera's view of the top of the building.
- Two intersections: The planet blocks the camera's view of the top of the building.
- One intersection: The point at which the top of the building appears or disappears.
There's only one such line that goes through the top of the building and intersects the outer rim of the circle only once. That line is a tangent to this circle. In other words, it is perpendicular to the radius of the circle at the point A where it touches the circle.
The camera needs to be on this tangent line when the building starts to disappear. To find the length of the arc that the robot has travelled, start by finding the angle
which corresponds to this minor arc.
This angle comes can be split into two parts:
.
Also,
.
The radius of this circle is:
.
The lengths of segment DC, AC, BC can all be found:
In the two right triangles
and
, the value of
and
can be found using the inverse cosine function:


.
The length of the minor arc will be:
.
Answer:
These atomos are called isotopes.
Explanation:
Each chemical element is characterized by the number of protons in its nucleus, which is called the atomic number (Z).
The number of neutrons in the nucleus can vary. There are almost always as many or more neutrons than protons. The atomic mass (A) is obtained by adding the number of protons and neutrons in a given nucleus.
The same chemical element can be made up of different atoms, that is, their atomic numbers are the same, but the number of neutrons is different. These atoms are called isotopes of the element. That is, isotopes are atoms whose atomic nuclei have the same number of protons but different numbers of neutrons.
So, <u><em>these atomos are called isotopes.</em></u>