Answer:
f = pl / (l + p)
Explanation:
1/f = 1/p + 1/l
Find the common denominator of the right hand side.
1/f = l/(pl) + p/(pl)
Add:
1/f = (l + p) / (pl)
Take the inverse of both sides:
f = pl / (l + p)
The force the box is exerting on Manuel is the weight of the box, downward:
and this force is perfectly balanced by the constraint reaction applied by Manuel's hand, pushing upward.
The average speed of the football is 15 meters per second. Just divide both of the numbers by 4 :)
Scientists measure the time between the arrival of an earthquake's __P____ and ___S____ waves to help determine the distance between the recording seismograph and the earthquake epicenter.
Explanation:
P- (compressional) and S- (shear) waves produced in earthquakes travel at different speeds. P waves are faster than S waves and hence will be detected first by a seismograph after an earthquake. The further away a seismograph is from the epicenter of an earthquake, the longer the time difference between the two (2) waves will be.
Using several, at least 3, seismographs located at different geoghraphical locations and detecting earthquakes, geologists can extrapolate the epicenter of an earthquake using the time differences in arrivals of the two waves in each of the seismographs, using the mathematics of triangulation.
Learn More:
For more on P- and S-- waves check out;
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Answer:
Distance = 345719139.4[m]; acceleration = 3.33*10^{19} [m/s^2]
Explanation:
We can solve this problem by using Newton's universal gravitation law.
In the attached image we can find a schematic of the locations of the Earth and the moon and that the sum of the distances re plus rm will be equal to the distance given as initial data in the problem rt = 3.84 × 108 m
Now the key to solving this problem is to establish a point of equalisation of both forces, i.e. the point where the Earth pulls the astronaut with the same force as the moon pulls the astronaut.
Mathematically this equals:
When we match these equations the masses cancel out as the universal gravitational constant
To solve this equation we have to replace the first equation of related with the distances.
Now, we have a second-degree equation, the only way to solve it is by using the formula of the quadratic equation.
We work with positive value
rm = 38280860.6[m] = 38280.86[km]
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The distance between the Earth and this point is calculated as follows:
re = 3.84 108 - 38280860.6 = 345719139.4[m]
Now the acceleration can be found as follows: