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Elis [28]
3 years ago
5

Four times as much as the sum of 1/5 and 2/3

Mathematics
1 answer:
Oxana [17]3 years ago
7 0

Answer:

4*[1/5+2/3]

4[3/15+10/15]

4[13/15]

4*13/15

=52/15

=3  7/15

Step-by-step explanation:

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A projectile is fired with muzzle speed 220 m/s and an angle of elevation 45° from a position 30 m above ground level. Where doe
Allushta [10]

Answer:

  • 4968.6 m from where it was fired
  • 221.33 m/s

Step-by-step explanation:

For the purpose of this problem, we assume ballistic motion over a stationary flat Earth under the influence of gravity, with no air resistance.

We can divide the motion into two components, one vertical and one horizontal. For muzzle speed s and launch angle θ, the horizontal speed is presumed constant at s·cos(θ). The initial vertical speed is then s·sin(θ) and the (x, y) coordinates as a function of time are ...

  (x, y) = (s·cos(θ)·t, -4.9t² +s·sin(θ)·t + h₀) . . . . . where h₀ is the initial height

To find the range, we can solve the equation y=0 for t, and use this value of t to find x.

Using the quadratic formula, we find t at the time of landing to be ...

  t = (-s·sin(θ) - √((s·sin(θ))²-4(-4.9)(h₀)))/(2(-4.9))

  t = (s/9.8)(sin(θ) +√(sin(θ)² +19.6h₀/s²))

For s = 220, θ = 45°, and h₀ = 30, the time of flight is ...

  t ≈ 31.939 seconds

Then the horizontal travel is

  x = 220·cos(45°)·31.939 ≈ 4968.6 . . . . meters

__

As it happens, the value under the radical in the above expression for time, when multiplied by s, is the vertical speed at landing. The horizontal speed remains s·cos(θ), so the resultant speed is the Pythagorean sum of these:

  landing speed = s·√(cos(θ)² +sin(θ)² +19.6h₀/s²) ≈ s√(1 +0.012149)

  ≈ 221.33 m/s

_____

Note that the landing speed represents the speed the projectile has as a consequence of the potential energy of its initial height being converted to kinetic energy that adds to the kinetic energy due to its initial muzzle velocity.

6 0
3 years ago
Choose the list that shows these numbers in order from smallest to largest.
svetlana [45]

Answer:

0.3, 0.32, 0.321, 0.345

Step-by-step explanation:

The maximum number of decimals shown in the series is 3.

Therefore, let's rewrite all the numbers with three decimal places.

0.32, 0.321, 0.3, 0.345 can be written as

0.320, 0.321, 0.300, 0.345

Now, we can easily compare the numbers and we can conclude:

0.300 < 0.320 < 0.321 < 0.345

Hence, the smallest to largest order is:

0.3, 0.32, 0.321, 0.345

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Step-by-step explanation:

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