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
hoa [83]
3 years ago
14

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

s the projectile hit the ground and with what speed?
Mathematics
1 answer:
Allushta [10]3 years ago
6 0

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.

You might be interested in
Please help me ASAP!!!​
Sergeu [11.5K]

Answer: 8

Because 8 - 11 = -3

Hope it helps.

3 0
3 years ago
Read 2 more answers
a vendor has 130,240and 150 oranges to put into bags so that each bag has the same number and there are no oranges left over.wha
almond37 [142]

is this multiple choice?

6 0
3 years ago
What is the Simplified form of √46/192
Lorico [155]

Answer:

  (√138)/24

Step-by-step explanation:

\displaystyle\sqrt{\frac{46}{192}}=\sqrt{\frac{46\cdot 3}{192\cdot 3}}=\sqrt{\frac{138}{24^2}}=\frac{\sqrt{138}}{24}

8 0
3 years ago
Which shape is similar to shape x?
alexandr1967 [171]

Answer:

<h2>the c one</h2>

Step-by-step explanation:

<h2>hope it will help</h2>
6 0
3 years ago
Read 2 more answers
What is the answer for 7-4x=2+x+6-5x
levacccp [35]

Answer:

no solution

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • Jordan jarred 18 liters of jam after 6 days. How many days does Jordan need to spend making jam if he wants to jar 27 liters of
    10·1 answer
  • An airliner maintaining a constant elevation of 2 miles passes over an airport at noon traveling 500 mi/hr due west. At 1:00 PM,
    13·1 answer
  • Plz help this is the only question I am stuck on.
    10·2 answers
  • A particle starts at the point P=(−5,−1,3) when t=0 and moves along a straight line toward Q=(−6,−6,8) at a speed of 9 cm/sec. L
    12·1 answer
  • What is the magnitude of an earthquake that is 5011 times more than a standard earthquake round the answer to the nearest 10th
    12·1 answer
  • Drag and drop numbers into the boxes so that the paired values are in a proportional relationship.
    13·2 answers
  • SOMEONE PLS HELP ME: The sum of three consecutive EVEN numbers is 48. What are the smallest of these numbers?
    10·2 answers
  • Please Help need ASAP
    9·2 answers
  • Out of these triangles which of them is a Right Triangle?<br> 4, 6, 10<br> 6, 8, 10<br> 10, 24, 26
    10·1 answer
  • 8 A clock in the shape of an hour glass is made up of two identical cones
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!