Answer:
0.061 J
Explanation:
The kinetic energy of an object is given by
where
m is the mass of the object
v is its speed
For the toy truck in the problem, we have
m = 0.1 kg is its mass
v = 1.1 m/s is its speed
Putting the numbers into the equation, we find
Answer:
F = M2 ω^2 R centripetal force of sun on planet
ω = (F / (M2 R))^1/2 = 2 pi f = 2 pi / P where P is the period
P = 2 pi (M2 * R / F)^1/2
F = G M1 M2 / R^2 gravitational force on planet
P = 2 pi {R^3 / (G M1)]^1/2
P = 6.28 [(2.0E11)^3 / (6.67E-11 * 3.0E30)]^1/2
P = 6.28 (8 / 20)^1/2 E7 = 3.9E7 sec
1 yr = 3600 * 24 * 365 = 3.15E7 sec
P = 3.9 / 3.2 = 1.2 years
Answer:
The answer is B
Explanation:
There are many Federal laws that help government tell scientist what is ethical and unethical.
The gravitational force between two objects is given by:
where
G is the gravitational constant
m1 and m2 are the masses of the two objects
r is their separation
In this problem, the first object has a mass of
, while the second "object" is the Earth, with mass
. The distance of the object from the Earth's center is
; if we substitute these numbers into the equation, we find the force of gravity exerted by the Earth on the mass of 0.60 kg:
Answer:at 21.6 min they were separated by 12 km
Explanation:
We can consider the next diagram
B2------15km/h------->Dock
|
|
B1 at 20km/h
|
|
V
So by the time B1 leaves, being B2 traveling at constant 15km/h and getting to the dock one hour later means it was at 15km from the dock, the other boat, B1 is at a distance at a given time, considering constant speed of 20km/h*t going south, where t is in hours, meanwhile from the dock the B2 is at a distance of (15km-15km/h*t), t=0, when it is 8pm.
Then we have a right triangle and the distance from boat B1 to boat B2, can be measured as the square root of (15-15*t)^2 +(20*t)^2. We are looking for a minimum, then we have to find the derivative with respect to t. This is 5*(25*t-9)/(sqrt(25*t^2-18*t+9)), this derivative is zero at t=9/25=0,36 h = 21.6 min, now to be sure it is a minimum we apply the second derivative criteria that states that if the second derivative at the given critical point is positive it means here we have a minimum, and by calculating the second derivative we find it is 720/(25 t^2 - 18 t + 9)^(3/2) that is positive at t=9/25, then we have our answer. And besides replacing the value of t we get the distance is 12 km.
