Velocity and Time

The angle of elevation from a point on the ground to the top of a pyramid is 37 degrees 50' The angle of elevation from a point

Serjik [45]

Answer:

The height of the pyramid is approximately 104 Ft. See the graphic attached.

Explanation:

First, you have to plot to realize that you have two rectangle triangles, formed by the different elevation points of view. From there you can have a system of two equations, with two unknown values.

Equation (1)

$tan 37^{o}50'= \frac{Ph}{x} \\\\Ph=tan 37^{o}50' x= 0.7766 x$

Equation (2)

$tan 18^{o}10'=\frac{Ph}{x+183} \\\\Ph=[tan 18^{o}10'][x+183]=[0.3281][x+183]$

Matching (1) and (2)

$0.7766 x=0.3281(x+183)\\\\(0.7766-0.3281)x=60.05\\\\x=\frac{60.05}{0.4485} =133.89ft$

replacing x value in (1)

$Ph=0.7766*133.89=103.9789\\Ph = 104 ft$

5 0

3 years ago

When a 4.25 kg object is placed on top of a vertical spring, the spring compresses a distance of 2.62 cm. what is the force cons

ANTONII [103]

The force applied to the spring is the weight of the object that compresses it, so it is equal to:
$W=mg=(4.25 kg)(9.81 m/s^2)=41.7 N$

Because of this force, the spring compresses by $x=2.62 cm=0.0262 m$ . Using Hook's law,
$F=kx$ ,
since we know the intensity of the force (the weight W) and the compression of the spring, x, we can find k, the spring constant:
$k= \frac{F}{x}= \frac{W}{x}= \frac{41.7 N}{0.0262 m} =1591.6 N/m$

6 0

3 years ago

Suppose a point charge is located at the center of a spherical surface. The electric field at the surface of the sphere and the

emmasim [6.3K]

Answer:

<em>The flux through the sphere will remain the same, and the magnitude of the electric field will increase by four times.</em>

Explanation:

The electric flux is the number of electric field, passing through a given area. It is proportional to the electric field strength and the area through which this field passes.

If the radius of the sphere is halved, the area of the sphere will reduce by square of the reduction, which will be four times. The electric field lines will become closer together, or technically increase by a fourth of its initial value. The resultant effect is that the electric flux will remain the same.

If originally,

Φ = EA cos∅

where Φ is the electric flux through the sphere

E is the electric field on the sphere

A is the area of the sphere.

If the area of the sphere is reduced to half, then,

the area reduces to A/4,

and the electric field increases to be 4E on the sphere.

The flux now becomes

Φ = 4E x A/4 cos∅

which reduces to

Φ = EA cos∅

which is the initial electric flux on the sphere.

8 0

2 years ago

Un cuerpo se lanza verticalmente hacia arriba con una velocidad de 13 m/s. ¿Cuánto tiempo tarda en alcanzar la altura máxima? a)

Elena L [17]

Answer:

D. 1.33 segundos.

Explanation:

El cuerpo es experimenta un movimiento en caída libre al modificarse su velocidad por efecto de la gravitación terrestre. Este cuerpo alcanza instantáneamente el reposo cuando se encuentra a su altura máxima, el tiempo puede obtenerse sabiendo la aceleración y las velocidades incial y final a partir de la siguiente ecuación cinemática:

$v = v_{o}+g\cdot t$

Donde:

$v$ - Velocidad final del cuerpo, medida en metros por segundo.

$v_{o}$ - Velocidad inicial del cuerpo, medida en metros por segundo.

$g$ - Aceleración gravitacional, medida en metros por segundo al cuadrado.

$t$ - Tiempo, medido en segundos.

Ahora se despeja el tiempo:

$t = \frac{v-v_{o}}{g}$

Si $v_{o} = 13\,\frac{m}{s}$ , $v=0\,\frac{m}{s}$ y $g = -9.807\,\frac{m}{s^{2}}$ , entonces:

$t = \frac{0\,\frac{m}{s}-13\,\frac{m}{s}}{-9.807\,\frac{m}{s^{2}} }$

$t = 1.326\,s$

Por ende, la respuesta correcta es D.

6 0

3 years ago

3. If a car is moving at 90km/hr and it rounds a corner, also at 90km/hr. Does it maintain

dolphi86 [110]

Answer:

Constant speed: yes

Constant velocity: no

Explanation:

Let's remind the definition of speed and velocity:

- Speed is a scalar quantity, which is equal to the ratio between the distance covered (regardless of the direction) and the time taken:

$s=\frac{d}{t}$

- Velocity is a vector quantity, so it has both a magnitude and a direction. The magnitude is equal to the rate between the displacement of the object and the time taken, while the direction is the same as the displacement.

In this problem, we notice that:

- The speed of the car remains constant, as it is 90 km/h

- However, its direction of motion changes while the car travels round the corner: this means that the direction of the velocity is also changing, therefore velocity is not constant.

8 0

3 years ago