Answer:
The observer sees the space-probe 9.055m long.
Explanation:
Let be the length of the space-probe when measured at rest, and
be its length as observed by an observer moving at velocity
, then
Now, we know that and
, and putting these into
we get:
Thus, an observer moving at 0.95c observes the space-probe to be 9.055m long.
Answer:
Explanation:
For this problem to be easier to calculate, we can represent the triangle as a right triangle whose right angle is located at the origin of a coordinate system. (See picture attached).
With this disposition of the triangle, we can start finding our integral. The hydrostatic force can be set as an integral with the following shape:
γhxdy
we know that γ=62.5 lb/
from the drawing, we can determine the height (or depth under the water) of each differential area is given by:
h=8-y
x can be found by getting the equation of the line, which we'll get by finding the slope of the line and using one of the points to complete the equation:
when substituting the x and y-values given on the graph, we get that the slope is:
once we got this slope, we can substitute it in the point-slope form of the equation:
which yields:
which simplifies to:
we can now solve this equation for x, so we get that:
with this last equation, we can substitute everything into our integral, so it will now look like this:
Now that it's all written in terms of y we can now simplify it, so we get:
we can now proceed and evaluate it.
When using the power rule on each of the terms, we get the integral to be:
By using the fundamental theorem of calculus we get:
When solving we get:
Answer:
Explanation:
First of all, let's remind that:
- The kinetic energy of an object is given by , where m is the mass and v is the speed
- The momentum of an object is given by
- The inertia of an object is proportional to its mass, so we can write , where k just indicates a constant of proportionality
In this problem, we have:
- (the two objects have same kinetic energy)
- (A has three times the momentum of B)
Re-writing both equation we have:
If we divide first equation by second one we get
And if we substitute it into the first equation we get
So, B has 9 times more mass than A, and so B has 9 times more inertia than A, and their ratio is:
Answer:
1) Time interval Blue Car Red Car
0 - 2 s Constant Velocity Increasing Velocity
2 - 3 s Constant Velocity Constant Velocity
3 - 5 s Constant Velocity Increasing Velocity
5 - 6 s Constant Velocity Decreasing Velocity
2) For Red and Blue car y₂ = 120 v = =
= 20 m/s
We get the same velocity for two cars because it is the average velocity of the car at the given interval of time. It is measured for initial and final position.
3) At t = 2s, the cars are the same position, and are moving at the same rate
Position - same
Velocity - same
The position-time graph shares the same spot for two cars.