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Elden [556K]
3 years ago
15

1.) A projectile is launched at 15 degrees. The landing height is the same as the launch position. At what other angle can the p

rojectile be launch to achieve the same horizontal displacement?
2.) A football is kicked into the air with a velocity of 32m/s at an angle of 25º. At the very top of the ball’s path, its vertical velocity is?
Physics
1 answer:
allsm [11]3 years ago
7 0
1) The general equations of motion of the projectile on the x and y axis are:
x(t) = v_0 \cos \alpha t
y(t)=v_0 \sin \alpha t -  \frac{1}{2}gt^2
where v0 is the initial velocity, \alpha is the angle with respect to the ground, and g=9.81 m/s^2 is the gravitational acceleration. We can see that the motion of the projectile is an uniform motion on the x-axis and an uniformly accelerated motion on the y-axis.

First, we need to find what is the total horizontal displacement of the projectile when it is launched with an angle of 15^{\circ}. To do that, we need to find first the time t at which the projectile lands to the ground, and we can find it by requiring y(t)=0:
v_0 \sin \alpha t -  \frac{1}{2}gt^2 =0
t( v_0 \sin \alpha -  \frac{1}{2} gt)=0
that has two solutions: t=0 (beginning of the motion) and
t= \frac{2 v_0 \sin \alpha}{g}
and this is the time after which the projectile lands to the ground. If we substitute this value into the equation for x(t), we find the total horizontal displacement of the projectile:
x_1=v_0 \cos \alpha t = v_0 \cos \alpha ( \frac{2 v_0 \sin \alpha }{g} )= \frac{2 v_0^2}{g} \sin \alpha \cos \alpha
with \alpha=15^{\circ}.

If we call \beta the other angle at which the projectile reaches the same horizontal displacement, the total horizontal displacement in this case is
x_2 =  \frac{2 v_0^2}{g} \sin \beta \cos \beta
Since the horizontal displacement should be the same in the two cases, we can write x1=x2, which becomes:
\sin \alpha \cos \alpha = \sin \beta \cos \beta
Now let's remind that \cos \theta= \sin (90^{\circ} -\theta) so that we can rewrite the equation as
\sin \alpha \sin (90^{\circ}-\alpha) = \sin \beta \sin (90^{\circ}-\beta)
and using \alpha=15^{\circ}:
\sin 15^{\circ} \sin (75^{\circ}) = \sin \beta \sin (90^{\circ}-\beta)
and we can see that there are two values of \beta that satisfy the equation: \beta=\alpha=15^{\circ} and \beta=75^{\circ}, which is the solution of our problem.

2) The vertical velocity of the ball at the very top of its trajectory is zero. In fact, the very top of the trajectory is the point where the ball starts to go down, so it means it is the moment when the the direction of the vertical velocity of the ball is changing from upward to downward, so it must be the moment when the vertical velocity is zero.
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The eye of the Atlantic giant squid has a diameter of 3.50 × 10^2 mm. If the eye
Lunna [17]

Answer:

   q = 224 mm,   h ’= - 98 mm, real imagen

Explanation:

For this exercise let's use the constructor equation

        \frac{1}{f} = \frac{1}{p} + \frac{1}{q}

       

where f is the focal length, p and q are the distance to the object and the image respectively.

In a mirror the focal length is

        f = R / 2

indicate us radius of curvature is equal to the diameter of the eye

       R = 3,50  10² mm

       f = 3.50 10² /2 = 1.75 10² mm

they also say that the distance to the object is p = 0.800 10³ mm

        1 / q = 1 / f - 1 / p

        1 / q = 1 / 175 - 1 /800

        1 / q = 0.004464

         q = 224 mm

to calculate the size let's use the magnification ratio

          m = \frac{h'}{h} = - \frac{q}{p}

          h '= - \frac{q}{p} \ h

          h ’= - 224 350 / 800

          h ’= - 98 mm

in concave mirrors the image is real.

3 0
3 years ago
Convertir:<br> A. 3Km a m<br> B. 250 ma Km<br> C. 1000Cm a m<br> D. 10000 mm a Cm
Katen [24]

Answer:

A. 3,000,000 m

B. 0.25 km

C. 10 m

D. 1,000 cm

Explanation:

no hablo español, así que solo ingrese esto en el traductor de G*ogle

A. One kilometer equals 1000 meters, so

3,000*1,000 = 3,000,000 m

B. One meter equals 0.001 kilometer, so

250*0.001 = 0.25 km

C. One centimeter equals 0.01 meter

1,000*0.01 = 10 m

D. One milimeter equals 0.1 centimer, so

10,000*0.1 = 1,000

4 0
3 years ago
A box weighing 52.4 N is sliding on a rough horizontal floor with a constant friction force of magnitude LaTeX: ff. The box's in
german

Answer:

The magnitude of the friction force exerted on the box is 2.614 newtons.

Explanation:

Since the box is sliding on a rough horizontal floor, then it is decelerated solely by friction force due to the contact of the box with floor. The free body diagram of the box is presented herein as attachment. The equation of equilbrium for the box is:

\Sigma F = -f = m\cdot a (Eq. 1)

Where:

f - Kinetic friction force, measured in newtons.

m - Mass of the box, measured in kilograms.

a - Acceleration experimented by the box, measured in meters per square second.

By applying definitions of weight (W = m\cdot g) and uniform accelerated motion (v = v_{o}+a\cdot t), we expand the previous expression:

-f = \left(\frac{W}{g} \right)\cdot \left(\frac{v-v_{o}}{t}\right)

And the magnitude of the friction force exerted on the box is calculated by this formula:

f = -\left(\frac{W}{g} \right)\cdot \left(\frac{v-v_{o}}{t}\right) (Eq. 1b)

Where:

W - Weight, measured in newtons.

g - Gravitational acceleration, measured in meters per square second.

v_{o} - Initial speed, measured in meters per second.

v - Final speed, measured in meters per second.

t - Time, measured in seconds.

If we know that W = 52.4\,N, g = 9.807\,\frac{m}{s^{2}}, v_{o} = 1.37\,\frac{m}{s}, v = 0\,\frac{m}{s} and t = 2.8\,s, the magnitud of the kinetic friction force exerted on the box is:

f = -\left(\frac{52.4\,N}{9.807\,\frac{m}{s^{2}} } \right)\cdot \left(\frac{0\,\frac{m}{s}-1.37\,\frac{m}{s}  }{2.8\,s} \right)

f = 2.614\,N

The magnitude of the friction force exerted on the box is 2.614 newtons.

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<h3>What is cause and effect relationship?</h3>

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A typical example of cause and effect relationship is that increased fossil  fuel use is leading to a rise in the average temperature of the planet.

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