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
Lorico [155]
3 years ago
11

During a fireworks display, a shell is shot into the air at an angle of theta degrees above the horizontal. The fuse is timed to

8.6 seconds for the shell just as it reaches its highest point above the ground. If the horizontal displacement of the shell is 81.7 meters when it explodes, what is the angle theta of the initial velocity
Physics
1 answer:
Klio2033 [76]3 years ago
7 0

Answer:

θ = 83.6º

Explanation:

  • Once the shell is in the air, the only influence acting on it (assuming that the resistance of the air is negligible) is gravity.
  • Gravity acts on the shell accelerating it in the vertical direction with a=g=-9.8 m/s2 (taking the upward direction as the positive one).
  • Since movements in perpendicular directions are independent each other, we conclude that in the horizontal direction, speed must be constant.
  • So, we can find the speed in the horizontal direction (the projection of the velocity vector along the horizontal axis) applying simply the definition of average velocity, as follows:

       v_{avg} =\frac{\Delta x}{\Delta t}  (1)

  • Taking the launch site as the origin, and making the horizontal direction coincident with the x-axis (positive to the right), we know that the horizontal displacement is 81.7 m, and the time at the explosion, 8.6 s, so we can write the horizontal component of the velocity vector (its projection along the x-axis) as follows:

       v_{x} = \frac{81.7m}{8.6s} = v_{o} * cos \theta = 9.5 m/s  (2)

  • In the vertical direction, since we know that the shell will explode when it reaches to the maximum height, at this point just before exploding, the vertical component of the velocity is just zero, even though it continues being accelerated downward.
  • Applying the definition of acceleration, replacing a by the value of g, we can write the following expression:

        v_{fy} = v_{oy} - g*t = v_{o} * sin \theta -g*t = 0   (3)

⇒      v₀* sin θ = g*t = 9.8m/s2* 8.6s = 84.3 m/s (4)

  • Dividing (4) by (2), we can find tg θ (the angle of the initial velocity with the x-axis), as follows:

       \frac{v_{o}* sin \theta}{v_{o}* cos \theta} = tg \theta= \frac{84.3m/s}{9.5m/s} = 8.87  (5)

⇒    θ = tg⁻¹ (8.87) = 83.6º

You might be interested in
Two coils close to each other have a mutual inductance of 32 mH. If the current in one coil decays according to I=I0e−αt, where
fiasKO [112]

The emf induced in the second coil is given by:

V = -M(di/dt)

V = emf, M = mutual indutance, di/dt = change of current in the first coil over time

The current in the first coil is given by:

i = i₀e^{-at}

i₀ = 5.0A, a = 2.0×10³s⁻¹

i = 5.0e^(-2.0×10³t)

Calculate di/dt by differentiating i with respect to t.

di/dt = -1.0×10⁴e^(-2.0×10³t)

Calculate a general formula for V. Givens:

M = 32×10⁻³H, di/dt = -1.0×10⁴e^(-2.0×10³t)

Plug in and solve for V:

V = -32×10⁻³(-1.0×10⁴e^(-2.0×10³t))

V = 320e^(-2.0×10³t)

We want to find the induced emf right after the current starts to decay. Plug in t = 0s:

V = 320e^(-2.0×10³(0))

V = 320e^0

V = 320 volts

We want to find the induced emf at t = 1.0×10⁻³s:

V = 320e^(-2.0×10³(1.0×10⁻³))

V = 43 volts

3 0
3 years ago
Explain an example of how energy is transferred from one form to another
scoray [572]

Answer:

read the explanation

Explanation:

Purchased electricity is fed into our TVs and is converted to light and sound.

Electricity goes into an electric bulb and is converted to visible light and heat energy.

Chemical Energy is converted to Electrical Energy (stove)

Chemical food energy is converted to Energy to Work (person running).

6 0
3 years ago
Theories have both an explanatory and a predictive function. <br> a. True <br> b. False
Simora [160]
Theories have both an explanatory an a predictive function. True
3 0
3 years ago
Read 2 more answers
A cyclical heat engine, operating between temperatures of 450º C and 150º C produces 4.00 MJ of work on a heat transfer of 5.00
gogolik [260]

Answer:

(a) Heat transfer to the environment is: 1 MJ and (b) The efficiency of the engine is: 41.5%

Explanation:

Using the formula that relate heat and work from the thermodynamic theory as:W=Q=Q_{in}-Q_{out} solving to Q_out we get:Q_{out}=Q_{in}-W=5(MJ)-4(MJ)=1(MJ) this is the heat out of the cycle or engine, so it will be heat transfer to the environment. The thermal efficiency of a Carnot cycle gives us: n=1-\frac{T_{Low} }{T_{High}} where T_Low is the lowest cycle temperature and T_High the highest, we need to remember that a Carnot cycle depends only on the absolute temperatures, if you remember the convertion of K=°C+273.15 so T_Low=150+273.15=423.15 K and T_High=450+273.15=723.15K and replacing the values in the equation we get:n=1-\frac{423.15}{723.15} =0.415=41.5%

5 0
3 years ago
The volume of an ideal gas changes from 0.40 to 0.55 m3 although its pressure remains constant at 50,000 Pa. What work is done o
Rama09 [41]

Answer:

w= p∆v 50000 ( 0.55-0.40) and calculate and you get it

7 0
3 years ago
Other questions:
  • What evidence supports a scientist's conclusion that fossil B is older than fossil A?
    15·2 answers
  • How does kinetic energy affect the stopping distance of a vehicle traveling at 30 mph compared to the same vehicle traveling at
    13·1 answer
  • How can i express 2.99792458 x10^8 in three insignificante figures
    6·1 answer
  • Which type of mechanical wave moves back and forth?
    10·2 answers
  • A fox runs for 12 seconds at a speed of 9.65 m/s. How much distance does it cover? Exact answer, do NOT round.
    9·1 answer
  • What is the correct answer choice? PLEASE HELP
    9·1 answer
  • A car starts from rest at a stop sign. It accelerates at 4.6 m/s^2 for 6.2 s , coasts for 2.1s , and then slows down at a rate o
    13·1 answer
  • How high off the ground is a 5.5 kg object that has a gravitational potential energy of 8500 DE=mah​
    8·1 answer
  • A toy dart gun has a spring with k= 128 N/m. How much force does it take to pull the spring back 0.0500 m? (Unit = N)​
    13·2 answers
  • A brick sliding across a smooth floor has a coefficient of static friction of s=0.23 and a coefficient of kinetic friction of k=
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!