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
horsena [70]
3 years ago
6

Suppose that you can throw a projectile at a large enough v0 so that it can hit a target a distance R downrange. Given that you

know v0 and R, determine the general expressions for the two distinct launch angles θ1 and θ2 that will allow the projectile to hit D. For v0 = 37 m/s and R = 70 m, determine numerical values for θ1 and θ2.
Engineering
1 answer:
viktelen [127]3 years ago
5 0

Answer:

\theta_1=15^o\\\theta_2=75^o

Explanation:

<u>Projectile Motion</u>

In projectile motion, there are two separate components of the acceleration, velocity and displacement. The horizontal component has zero acceleration (assuming no friction), and the acceleration in the vertical direction is always the acceleration of gravity. The basic formulas are shown below:

V_x=V_{ox}=V_ocos\theta

Where \theta is the angle of launch respect to the positive horizontal direction and Vo is the initial speed.

V_y=V_{oy}-gt=V_osin\theta-gt

The  horizontal and vertical distances are, respectively:

x=V_{o}cos\theta t

\displaystyle y=y_o+V_{o}sin\theta t-\frac{gt^2}{2}

The total flight time can be found as that when y = 0, i.e. when the object comes back to ground (or launch) level. From the above equation we find

\displaystyle t_f=\frac{2V_osin\theta}{g}

Using this time in the horizontal distance, we find the Range or maximum horizontal distance:

\displaystyle R=\frac{V_o^2sin2\theta}{g}

Let's solve for \theta

\displaystyle sin2\theta=\frac{R.g}{V_o^2}

This is the general expression to determine the angles at which the projectile can be launched to hit the target. Recall the angle can have to values for fixed positive values of its sine:

\displaystyle \theta_1=\frac{asin\left(\frac{R.g}{V_o^2}\right)}{2}

\displaystyle \theta_2=\frac{180^o-asin\left(\frac{R.g}{V_o^2}\right)}{2}

Or equivalently:

\theta_2=90^o-\theta_1

Given Vo=37 m/s and R=70 m

\displaystyle \theta_1=\frac{asin\left(\frac{70\times 9.8}{37^2}\right)}{2}

\theta_1=15^o

And

\theta_2=90^o-15^o=75^o

You might be interested in
What is the best reason a scientist might use a model to represent the solar system?
uranmaximum [27]
So they can grasp a better understanding! good luck
3 0
3 years ago
Microchips found inside most electronic devices today are examples of what material A. Polymers B. Alloys C. Composites D. None
dedylja [7]

Answer: A

Explanation:

Microchips are made out of silicone witch is a polymer.

6 0
3 years ago
Read 2 more answers
Calculate the ratio of change in the mass of the molecules of a gas to the initial mass, if its
kirill115 [55]

<h2>Answer:</h2>

<h3>Required Answer is as follows :-</h3>

  • \sf \dfrac{P _{i}}{ P_{f}} = \dfrac{3}{4}

  • 3/4 = (⅓ × m₁/Volume × V²)/(⅓ × m₂/Volume) × (V/2)²

  • ¾ = m₁/Volume × (V)²/m₂/Volume × (V/2)²

  • ¾ = m₁ × (V)²/m₂ × (V²/4)

  • ¾ = m₁/m₂ × 4

  • m₂ = 4 × 4/3 = 16/3m₁

\bold{   } 

<h3>Now,</h3>
  • ∆m = m₂ - m₁
  • ∆m = 16m₂/3 - m₁ = 13m₁/3
  • Ratio = (13m₁/3)/ m₁
  • Ratio = 13/3

Ratio = 13:3

\bold{   } 

<h3>Know More :-</h3>

Mass => It is used to measure it's resistance to its acceleration. SI unit of mass is Kg.\bold{   } 

3 0
3 years ago
What are some goals of NYFEA? Select three options.
faltersainse [42]

Answer:

developing agricultural leaders

encouraging new and young farmers

encouraging small farms

7 0
2 years ago
Read 2 more answers
If a construction company is considering a new type of material to use in their construction, which factors would they
Amanda [17]

I would honestly select every one of the given options. Gor a company evaluating this new material it would be very valuable to hit each of these factors.

4 0
2 years ago
Other questions:
  • A sand has a natural water content of 5% and bulk unit weight of 18.0 kN/m3. The void ratios corresponding to the densest and lo
    6·1 answer
  • Liquid water enters a valve at 300 kPa and exits at 275 kPa. As water flows through the valve, the change in its temperature, st
    10·1 answer
  • The working section of a transonic wind tunnel has a cross-sectional area 0.5 m2. Upstream, where the cross-section area is 2 m2
    10·1 answer
  • a vertical cylindrical container is being cooled in ambient air at 25 °C with no air circulation. if the initial temperature of
    12·2 answers
  • Thermosets burn upon heating. a)-True b)- false?
    10·1 answer
  • A three-point bending test is performed on a glass specimen having a rectangular cross section of height d = 5.4 mm (0.21 in.) a
    6·1 answer
  • What does this middle button on the middle of my Chevrolet equinox steering wheel mean?
    12·2 answers
  • Which of the following parts tells the transmission how fast or slowly a vehicle is going? A) pump
    5·1 answer
  • Select the correct answer.
    11·1 answer
  • 8. What are used by the project architect to depict different building systems and to show how they correlate to one anothe
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!