1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
If the mass of a materials is 44grams and the volume of the material is 11cm^3 what would the density of the material be
jok3333 [9.3K]
Density =mass/volume
density= (0.044kg/(11 x10^-6)
4000kg/m^3
8 0
3 years ago
PLEASE HELP ASAP! THANKS!<br><br> Why is it a rare occasion to see a solar eclipse from your home?
Y_Kistochka [10]

Answer:

It is very rare to see a solar eclipse from your home, because the Earth, Sun, and the moon need to align just right.  Not everyone in the world can view a solar eclipse, only some area can.  A solar eclipse is where the moon blocks out the sun.  If you think about it:  Let's say you live in Florida, U.S.A.  You may see the moon coming in front of the sun, but if you lived in California or sumthin', the moon and the sun wouldn't be aligned to form a solar eclipse.  It all depends on location... so it is rare to see one.

5 0
3 years ago
A 4.6 g lead bullet moving at 278 m/s strikes a steel plate and stops. If all its kinetic energy is converted to thermal energy
iren2701 [21]

Answer:

ΔT = 302 °c

Explanation:

mass (m) = 4.6 g = 0.0046 kg

velocity (v) = 278 m/s

specific heat of lead (c) = 128 J/kg. °c

kinetic energy = 0.5 mx v^{2}

kinetic energy = 0.5 x 0.0046 x 278^{2}

kinetic energy = 177.8 J

since all the kinetic energy is converted to thermal energy,

kinetic energy = thermal energy (E) = 177.8 J

thermal energy = m x c x ΔT

where ΔT is the temperature change

177.8 = 0.0046 x 128 x ΔT

ΔT = 177.8 / 0.59

ΔT = 302 °c

3 0
3 years ago
The energy that's given to the body by food is A. measured in units called calories. B. best obtained by eating high protein. C.
mel-nik [20]

Answer:

Calories, however you might want to back up my answer. I havent studied this topic in a while.

4 0
3 years ago
The cable of a crane is lifting a 750 kg girder. The girder increases its speed from 0.25 m/s to 0.75 m/s in a distance of 3.5 m
IgorC [24]

To solve this exercise it is necessary to apply the equations concerning Work, both by general definition and by conservation of energy.

In other words, the work done by an object due to gravity is the equivalent to that defined by the potential energy equations, that is

W= mg\Delta h

Where,

m=mass

g=gravitational acceleration

\Delta h = Change in height

On the other hand we have that the work done by tension is defined by the conservation of kinetic and potential energy, that is to say

W= \Delta KE + \Delta PE

Where,

\Delta KE = Change in Kinetic Energy

\Delta PE =Change in Potential Energy

PART A) As defined by the work done by gravity would be given by,

W = mg\Delta h

W = (750)(9.8)(3.5)

W = 25.725kJ

Therefore the work done by gravity is 25.725kJ

PART B) The work done by the tension applies the energy conservation equation, that is to say

W= \Delta KE + \Delta PE

W = (\frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2)+(mgh_f-mgh_i)

W = \frac{1}{2}m(v_f^2-v_i^2)+mg(h_f-h_i)

Replacing with our values,

W = \frac{1}{2}(750)(0.75^2-0.25^2)+(750)(9.8)(3.5)

W = 25.912kJ

Therefore the work done by tension is 25.9kJ

5 0
3 years ago
Other questions:
  • It turns out that Mercury and Mars have the same gravity as one another – that is, you would weigh the same on the surface of Me
    15·1 answer
  • If a much heavier stone rolled off the same cliff, would it hit the ground more quickly? explain
    12·2 answers
  • a 300kg motorboat is turned off as it approaches a dock and coasts towards it at .5 m/s. Isaac, whose mass is 62 kg jumps off th
    10·1 answer
  • How does energy acquisition in the deep sea differ from energy acquisition near the ocean’s surface? a. Organisms in the deep se
    13·2 answers
  • A 0.750kg block is attached to a spring with spring constant 13.5N/m . While the block is sitting at rest, a student hits it wit
    13·1 answer
  • A school bus moves past a parked car at a speed of 30 km/hr. Which of the following BEST describes the observation made by a pas
    7·1 answer
  • an ice skater applies a horizontal force to a 20.-kilogram block on frictionless, level ice, causing the block to accelerate uni
    11·1 answer
  • Question 6 (5 points)
    13·1 answer
  • Which statement is true of gravity?
    10·1 answer
  • Which of the following terms describes a process for which Q = -73 J?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!