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3 years ago

Does the horizontal motion of the projectile depend on the vertical motion?

2 answers:

8 0

Projectile motion follows a curved path created because of the gravity acting on the otherwise eternally traveling horizontal object, Can not necessarily say it depends on it, but it is a defining aspect of the projectile motion definition.

bezimeni [28]3 years ago

4 0

No, resolve in both directions separately

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A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 6 ft from the path and is kept fo

BARSIC [14]

We are given that,

$\frac{dx}{dt} = 4ft/s$

We need to find $\frac{d\theta}{dt}$ when $x=8ft$

The equation that relates x and $\theta$ can be written as,

$\frac{x}{6} tan\theta$

$x = 6tan\theta$

Differentiating each side with respect to t, we get,

$\frac{dx}{dt} = \frac{dx}{d\theta} \cdot \frac{d\theta}{dt}$

$\frac{dx}{dt} = (6sec^2\theta)\cdot \frac{d\theta}{dt}$

$\frac{d\theta}{dt} = \frac{1}{6sec^2\theta} \cdot \frac{dx}{dt}$

Replacing the value of the velocity

$\frac{d\theta}{dt} = \frac{1}{6} cos^2\theta (4)^2$

$\frac{d\theta}{dt} = \frac{8}{3} cos^2\theta$

The value of $cos \theta$ could be found if we know the length of the beam. With this value the equation can be approximated to the relationship between the sides of the triangle that is being formed in order to obtain the numerical value. If this relation is known for the value of x = 6ft, the mathematical relation is obtained. I will add a numerical example (although the answer would end in the previous point) If the length of the beam was 10, then we would have to

$cos\theta = \frac{6}{10}$

$\frac{d\theta}{dt} = \frac{8}{3} (\frac{6}{10})^2$

$\frac{d\theta}{dt} = \frac{24}{25}$

Search light is rotating at a rate of 0.96rad/s

4 0

3 years ago

A model train engine was moving at a constant speed on a straight horizontal track. As the engine moved along, a marble was fir

bagirrra123 [75]

Answer:

The marble was moving in a projectile and the speed of the engine was 2.716 m/s

Explanation:

The vertical component of the marble's flight path relative to the train

is given by the equation y(t) = v*t - (4.9)*t^2,

where, v is the initial upward velocity of the marble relative to the train.

So with y(1) = v - 4.9 = 0 we have

v = 4.9 m/s.

The marble will reach maximum height after 0.5 seconds, at which the

height will be y(0.5) = (4.9)*(0.5) - (4.9)*(0.5)^2 = (4.9)*(0.25) = 1.225 m.

Now, the marble has a vertical velocity component of 4.9 m/s and a horizontal velocity component

of V m/s such that tan(61) = 4.9 / V

V = 4.9 / tan(61) = 2.716 m/s

This horizontal velocity component of the marble is the same as the

speed of the train i.e. 2.716 m/s.

3 0

4 years ago

If there is a break at any point in a series circuit the current will

Tomtit [17]

Answer:

not work

Explanation:

in a series circuit, everything meaning the electrons are flowing on one path, therefore, it wouldn continue to work.

8 0

3 years ago

Which is the phase change in which a substance changes from a gas to liquid?

Aleksandr [31]

Answer:

Condensation

Explanation:

The phase change in which a substance changes from a gas to liquid is Condensation.

There are 3 natural states of matter;

Solids, Liquids, and Gases.

Matter under certain conditions can change from one state to another. When Solids are heated they change into Liquids through the process of Heating. Upon cooling, the Liquids convert to Solid through freezing. When a Liquid such as water is heated, it converts into the Gaseous state through evaporation. Upon cooling, the Gas converts back into the Liquid state through Condensation.

3 0

3 years ago

If an object is not accelerating what can you determine about the sum of all the forces on the object

xxTIMURxx [149]

If object is not accelerating, the sum of all forces on the object will be equal to ZERO...

8 0

4 years ago