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marishachu [46]
3 years ago
13

The x-coordinates of two objects moving along the x-axis are given as a function of time t. x1 = (4 m/s)t and x2 = −(159 m) + (2

4 m/s)t − (1 m/s2)t2 . Calculate the magnitude of the distance of closest approach of the two objects. x1 and x2 never have the same value.

Physics
1 answer:
SpyIntel [72]3 years ago
3 0
The x-coordinate of the first object is
x₁(t) = (4 m/s)t

The x-coordinate of the second object is
x₂(t) = -(159 m) + (24 m/s)t - (1 m/s²)t²

The distance between the two objects is
x(t) = x₂ - x₁ 
      =  - 159 + 24t - t² - 4t
      = -t² + 20t  - 159

Write this equation in the standard form for a parabola.
x = -[t² - 20t] - 159
   = -[(t - 10)² - 100] - 159
   = -(t-10)² - 59

This parabola has a vertex at (-10,  -59), and it is downward.
Because the maximum value of x is negative, the two objects never touch
The closest distance between the objects is 59 m.

The two graphs confirm that the analysis is correct.

Answer: The closest approach is 59 m.

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If you're referring to the different colors that usually occur at the tip of missles, rockets and some other aircraft, it either a) signifies the end of a particular plate of metal, fabricated specifically to be for the nose. Sometimes these can even be a different alloy or metal all together. or b) this shows where the curved surface begins, so in the case of damage or imperfections due to wear, they can be repaired and measured more easily. The shape of the nose is extremely important for smooth flight, and a dent or bump formed on it can make the aircraft unstable. If you can measure from where the curve starts by the difference in color, it makes repairing or re-fabricating the part much easier. Many of these curves aren't as simple as they appear.
5 0
3 years ago
vector u has a magnitude of 20 and direction of 0°.vector v has amagnitude of 40and a direction of 60°.find the magnitude and di
pantera1 [17]

Addition of vectors:

vector u

has a magnitude of 20 and a direction of 0º with respect to the horizontal, vector v has a magnitude of 40 and a direction of 60º with respect to the horizontal.

a) Find the magnitude and direction of the resultant to the nearest whole

number.

Vector Sum:

The resultant of two vectors is simply the vector sum of the vectors. There are a handful of ways to present the resultant factor; the notation that shows the vector magnitude and direction is called the polar vector notation. An example of a vector presented in polar vector notation is

a∠θ where a is the magnitude and θis the angle that the vector makes with the horizontal axis.

Answer and Explanation:

Let's first present the vectors in rectangular vector notation.

For the vector →u of magnitude 20 and direction 0∘ to the horizontal axis, the vector is →u=^i20.

For the vector →v

of magnitude 40 and direction 60∘ to the horizontal axis, the vector is →v=^i40cos60∘+^j40sin60∘.

The resultant vector →w is the vector sum of the vectors, i.e.

→w=→u+→v

=^i20+^i40cos60∘+^j40sin60∘

=^i(20+40cos60∘)+^j(40sin60∘)

=^i40+^j20√3

For a vector ^ix+^jy, the magnitude of the vector is √x2+y2 and the direction above the horizontal axis is θ=tan−1(yx).

Let's use the formulas:

|→w|∠θ=√(40)2+(20√3)2∠tan−1(20√340)≈52.9∠40.9∘

The magnitude of the vector is about 53 units in the direction 41-degrees above the horizontal axis.

6 0
3 years ago
When a certain string is clamped at both ends, the lowest four resonant frequencies are 50, 100, 150, and 200 Hz. When the strin
mario62 [17]

Answer:

Explanation:

Given

Lowest four resonance frequencies are given with magnitude

50,100,150 and 200 Hz

The frequency of vibrating string is given by

f=\frac{n}{2L}\sqrt{\frac{T}{\mu }}

where n=1,2,3 or ...n

L=Length of string

T=Tension

\mu =Mass per unit length

When string is clamped at mid-point

Effecting length becomes L'=0.5 L

Thus new Frequency becomes

f' =\frac{n}{L}\sqrt{\frac{T}{\mu }}

i.e. New frequency is double of old

so new lowest four resonant frequencies are 100,200,300 and 400 Hz      

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3 years ago
What type of rock can melt to form magma
navik [9.2K]
Igneous rock your welcome
3 0
3 years ago
A particular radio station broadcast radio waves at 100 MHz (100 million Hz). If the radio waves travel at the speed of light (3
Svetlanka [38]


Wavelength  =  (speed) / (frequency)


                      =  (3 x 10⁸ m/s) / (1 x 10⁸ /s)  =  3 meters 

4 0
3 years ago
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