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umka21 [38]
3 years ago
14

If the range of the projectile is 4.3 m, the time-of-flight is T = 0.829 s, and air resistance is negligible, determine the foll

owing.a. What is the launch angle of the projectile?b. What is the initial speed of the projectile?c. Express the maximum height reached by a projectile like the one in this problem but with any range and time of flight in terms of g and T.
Physics
1 answer:
ankoles [38]3 years ago
7 0

Answer

given,

range of the projectile = 4.3 m

time of flight = T = 0.829 s

v =\dfrac{d}{T}

v =\dfrac{4.3}{0.829}

     v = 5.19 m/s

vertical component of velocity of projectile

v_y = gt'

v_y = 9.8 \times {\dfrac{T}{2}}

v_y = 9.8 \times {\dfrac{0.829}{2}}

v_y =4.06\ m/s

a) Launch angle

 \theta = tan^{-1}(\dfrac{v_y}{v})

 \theta = tan^{-1}(\dfrac{4.06}{5.19})

    θ = 38°

b) initial speed of projectile

  v = \sqrt{v_x^2 + v_y^2}

  v = \sqrt{5.19^2 + 4.06^2}

         v = 6.59 m/s

c) maximum height reached by the projectile

     y_{max}=v_{avg}t'

     y_{max}=\dfrac{1}{2}v_y\dfrac{T}{2}

     y_{max}=\dfrac{1}{2}\times(g\dfrac{T}{2})\times\dfrac{T}{2}

     y_{max}=\dfrac{gT^2}{8}          

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Which device is using a motor? A. A water heater creates heat energy from electric energy. B. A waterfall rotates a waterwheel t
Mumz [18]

Answer:

C is the right answer.

Body massager uses electrical energy to move back and forth. In this sense, a motor is being used for the operation

4 0
3 years ago
A long, thin solenoid has 450 turns per meter and a radius of 1.06 . The current in the solenoid is increasing at a uniform rate
kirill115 [55]

Answer:9.34 A/s

Explanation:

Given

radius of solenoid R=1.06 m

Emf induced E=8.50\times 10^{-6} V/m

no of turns per meter n=450

we know Induced EMF is given by

\int Edl=-\frac{\mathrm{d} \phi}{\mathrm{d} t}=-\frac{\mathrm{d} B}{\mathrm{d} t}A

Magnetic Field is given by

B=\mu _0ni

thus \frac{\mathrm{d} B}{\mathrm{d} t}=-\mu _0n\frac{\mathrm{d} i}{\mathrm{d} t}

Area of cross-section

A=\pi R^2 where

solving integration we get

E.\cdot 2\pi r=\mu _0n\frac{\mathrm{d} i}{\mathrm{d} t}\pi R^2

where r=distance from axis

R=radius of Solenoid

\frac{\mathrm{d} i}{\mathrm{d} t}=\frac{Er}{\mu _0nR^2}

\frac{\mathrm{d} i}{\mathrm{d} t}=\frac{8.50\times 10^{-6}\times 3.49\times 10^{-2}}{4\pi \times 10^{-7}\times 450\times 1.06^2}

\frac{\mathrm{d} i}{\mathrm{d} t}=9.34 A/s

4 0
3 years ago
May
GalinKa [24]

Answer:

a)  t = 0.90 s, b)  t = 0.815 s, c)  t = 0.90 s, d)  x = 3.6 m, e)  t = 0.639 s

Explanation:

all these exercises are about kinematics

a) The body is released from rest,  

           y = y₀ + v₀ t - ½ g t²

in this case when reaching the ground y = 0 and its initial velocity is vo = 0

           0 = y₀ + 0 - ½ g t²

           t² = 2 y₀ / g

           t² = 2 4 /9.81

           t² = 0.815

            t = √0.815

           t = 0.90 s

b) It is thrown upwards at v₀ = 4 m / s

         y = y₀ + v₀ t - ½ g t²

in this case the initial and final height is the same

        y = y₀ = 0

        0 = v₀ t -1/2 g t²

        t = 2 v₀ / g

        t = 2 4 /9.81

        t = 0.815 s

c) the ball is at y₀ = 4 m and its initial velocity is horizontal v₀ = 4 m / s

        y = y₀ + v_{oy} t - ½ g t²

        0 = y₀ + 0 - ½ g t²

        t² = 2 i / g

        t² = 2 4 / 9.81

        t² = 0.815

        t = 0.90 s

d) the horizontal distance traveled is

        x = v₀ₓ t

        x = 4 0.90

        x = 3.6 m

e) We can calculate the time to fall from I = 2 m

        y = y₀ + v_{oy} t - ½ g t²

        0 = y₀ + 0 - ½ g t²

        t² = 2 y₀i / g

        t² = 2 2 /9.81

        t² = 0.4077

        t = 0.639 s

Therefore, when making measurements, you should find readings around this value.

8 0
3 years ago
A grating that has 3900 slits per cm produces a third- order fringe at a 28.0° angle. What wavelength of light is being used? Ex
Zolol [24]

Explanation:

Given that,

Number of slits per cm, N=3900\ lines/cm=390000\lines/m

The third fringe is obtained at an angle of, \theta=28

We need to find the wavelength of light used. The grating equation is given by :

d\ sin\theta=n\lambda

d=\dfrac{1}{N}=\dfrac{1}{390000}

d=2.56\times 10^{-6}\ m

\lambda=\dfrac{d\ sin\theta}{n}, n = 3

\lambda=\dfrac{2.56\times 10^{-6}\times \ sin(28)}{3}

\lambda=4.006\times 10^{-7}\ m

\lambda=400\ nm

So, the wavelength of the light is 400 nm. Hence, this is the required solution.

4 0
3 years ago
Near the end of a marathon race, the first two runners are separated by a distance of 45.0 m. The front runner has a velocity of
xxMikexx [17]

Answer:

a. 0.7 m/s

b. The second runner

c. 4.20 meters

Explanation:

a. To know the relative speed we can use the following equation:

Relative Speed (Vr) = V1 - V2

The relative speed is used to compared the velocity of one object (V1) to another object (V2). To learn the Relative Velocity from the second runner to the first we do the following:

Relative Speed (Vr) = Second Runner Velocity (Vs) - First Runner Velocity (Vf)

Vr = 4.20 m/s  - 3.50 m/s

Vr = 0.7 m/s

This means that the second runner is gaining 0.7 meter from the first runner each second.

b. To know which runner will gain the race, we need to keep in mind, that the seconds runner is 45 meter more away that the first runner from the goal. Knowing this, the winner will be the one that reach the goal on less time.

Because movement is constant, we can use the following equation:

Velocity (V) = Distance (D) / Time (T)

To get the time we do:

T = D / V

Now, for the first runner:

T = 250 meters / (3.50 m/s)

T = 71.42 seconds

For the second runner.

T = (250 meters + 45 meters) / (4.20 m/s)

T = 70,23 seconds

Because the second runner takes less time to reach the goal, he wins the race.

c. Because it is know how much time takes the winner to get to the finish line, we can use that same time to know how far was the first runner from the goal. This is posible we know that how far he is from the goal is as follows.

Distance from goal (Dg) = Total Distance (D) - Distance travelled (Dt)

Where Total Distance (D) is 250 mts. And the distance travelled can be obtained by using the following equation.

Velocity (V) = Distance (D) / Time (T)

Searching for distance:

D = V / T.

D = (3.50 m/s) * 70.23 s

D = 245,80 meters

Soo

Distance from goal (Dg) = Total Distance (D) - Distance travelled (Dt)

Dg = 250 meters - 245,80 meters

Dg = 4,20 meters

The first runner was 4,20 meter behind the second one when the second runner crossed the goal

3 0
3 years ago
Read 2 more answers
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