If you had to explain to a non-scientist why it is that scientists accept the idea that all material things are composed of atom
1 answer:
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Answer:
a) The rocket reaches a maximum height of 737.577 meters.
b) The rocket will come crashing down approximately 17.655 seconds after engine failure.
Explanation:
a) Let suppose that rocket accelerates uniformly in the two stages. First, rocket is accelerates due to engine and second, it is decelerated by gravity.
1st Stage - Engine
Given that initial velocity, acceleration and travelled distance are known, we determine final velocity (), measured in meters per second, by using this kinematic equation:
(1)
Where:
- Acceleration, measured in meters per square second.
- Travelled distance, measured in meters.
- Initial velocity, measured in meters per second.
If we know that ,
and
, the final velocity of the rocket is:
The time associated with this launch (), measured in seconds, is:
2nd Stage - Gravity
The rocket reaches its maximum height when final velocity is zero:
(2)
Where:
- Initial speed, measured in meters per second.
- Final speed, measured in meters per second.
- Gravitational acceleration, measured in meters per square second.
- Initial height, measured in meters.
- Final height, measured in meters.
If we know that ,
,
and
, then the maximum height reached by the rocket is:
The rocket reaches a maximum height of 737.577 meters.
b) The time needed for the rocket to crash down to the launch pad is determined by the following kinematic equation:
(2)
Where:
- Initial height, measured in meters.
- Final height, measured in meters.
- Initial speed, measured in meters per second.
- Gravitational acceleration, measured in meters per square second.
- Time, measured in seconds.
If we know that ,
,
and
, then the time needed by the rocket is:
Then, we solve this polynomial by Quadratic Formula:
,
Only the first root is solution that is physically reasonable. Hence, the rocket will come crashing down approximately 17.655 seconds after engine failure.
Answer:
Option D: 21.8 degrees
Explanation:
In a parallel RL circuit, the current in the resistor R and that in the inductor L are separated among themselves 90 degrees as illustrated in the attached image. In the image the current in the resistor is represented in orange, that of the inductor in blue, and the total current (vector addition of the previous two) is represented in red, forming a certain angle (theta) with respect to the current in the resistor. The output voltage is the same as the input voltage as measured over the resistor R.
Therefore, the phase angle that separated output voltage and total current can be obtained using the fact that tan(phase angle) = , therefore the angle is the arctangent of 4/10:
degrees.
