Please help me , I also have to show work on paper

A 12,500 N alien UFO is hovering about the surface of Earth. At time , its position can be given as () = ((0.24 m/s^3)^3 + 25 m)

stepladder [879]

a) $F=(3675i-4543k)N$

b) 5843 N

Explanation:

a)

The position of the UFO at time t is given by the vector:

$r(t)=(0.24t^3+25)i+(4.2t)j+(-0.43t^3+0.8t^2)k$

Therefore it has 3 components:

$r_x=0.24t^3+25\\r_y=4.2t\\r_z=-0.43t^3+0.8t^2$

We start by finding the velocity of the UFO, which is given by the derivative of the position:

$v_x=r'_x=\frac{d}{dt}(0.24t^3+25)=3\cdot 0.24t^2=0.72t^2\\v_y=r'_y=\frac{d}{dt}(4.2t)=4.2\\v_x=r'_z=\frac{d}{dt}(-0.43t^3+0.8t^2)=-1.29t^2+1.6t$

And then, by differentiating again, we find the acceleration:

$a_x=v'_x=\frac{d}{dt}(0.72t^2)=1.44t\\a_y=v'_y=\frac{d}{dt}(4.2)=0\\a_z=v'_z=\frac{d}{dt}(-1.29t^2+1.6t)=-2.58t+1.6$

The weight of the UFO is W = 12,500 N, so its mass is:

$m=\frac{W}{g}=\frac{12500}{9.8}=1276 kg$

Therefore, the components of the force on the UFO are given by Newton's second law:

$F=ma$

So, Substituting t = 2 s, we find:

$F_x=ma_x=(1276)(1.44t)=(1276)(1.44)(2)=3675 N\\F_y=ma_y=0\\F_z=ma_z=(1276)(-2.58t+1.6)=(1276)(-2.58(2)+1.6)=-4543 N$

So the net force on the UFO at t = 2 s is

$F=(3675i-4543k)N$

b)

The magnitude of a 3-dimensional vector is given by

$|v|=\sqrt{v_x^2+v_y^2+v_z^2}$

where

$v_x,v_y,v_z$ are the three components of the vector

In this problem, the three components of the net force are:

$F_x=3675 N\\F_y=0\\F_z=-4543 N$

Therefore, substituting into the equation, we find the magnitude of the net force:

$|F|=\sqrt{3675^2+0^2+(-4543)^2}=5843 N$

7 0

3 years ago

A ball, with a mass of 5.9kg, is thrown directly upwards. It reaches a maximum height of 10m from the point at which it was rele

katrin2010 [14]

Answer:

14 m/s

Explanation:

We can solve the problem by using the law of conservation of energy.

At the beginning, when the ball is thrown from the ground, it has only kinetic energy, which is given by

$K=\frac{1}{2}mv^2$

where m = 5.9 kg is the mass of the ball and v is its initial speed.

As the ball goes up, its speed decreases, so its kinetic energy decreases and converts into gravitational potential energy. When the ball reaches its maximum height, the speed has become zero, and all the kinetic energy has been converted into gravitational potential energy, given by:

$U=mgh$

where g = 9.8 m/s^2 is the gravitational acceleration and h = 10 m is the maximum height reached by the ball.

Since we can ignore air resistance, energy must be conserved, so the initial kinetic energy must be equal to the final potential energy of the ball, so we can write:

$K=U\\\frac{1}{2}mv^2=mgh$

And we can solve the equation to find v, the initial speed of the ball:

$v=\sqrt{2gh}=\sqrt{2(9.8 m/s^2)(10 m)}=14 m/s$

8 0

3 years ago

PHYSICS

quester [9]

Answer:

c) 8.3 x 10^24 molecules

Explanation:

First of all, we convert the volume of the glass of water from mL to $cm^3$ :

$V=250 mL = 250 cm^3$

The relationship between mass and volume is:

$d=\frac{M}{V}$

where

$d=1.00 g/cm^3$ is the density of water

M is the total mass of the glass of water

$V=250 cm^3$ is the volume of the water in the glass

Solving for M,

$M=dV=(1.00)(250)=250 g = 0.250 kg$

Now we know that the mass of a single molecule of water is

$m=3.0\cdot 10^{-26}kg$

The total mass of the water in the glass can be written as

$M=Nm$

where

N is the number of molecules in the glass of water

Solving for N, we find:

$N=\frac{M}{m}=\frac{0.250}{3.0\cdot 10^{-26}}=8.3\cdot 10^{24}$

7 0

3 years ago

Which term is defined as a change in an object's position relative to a reference point?

Gre4nikov [31]

The answer would be REFERENCE POINT

4 0

3 years ago

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Four aqueous solutions and their concentrations are shown in the above illustration. which of the solutions is most likely to be

Elza [17]

The solution that would most likely be a strongest conductor of electricity is the solution that is most saturated or concentrated. This is because the atoms that are found within the aqueous solutions have become positively charged resulting to the attraction of negatively charged ions that are found in electricity. On the other hand, the least conductive from the aqueous solutions would be the most unsaturated one because of less conductive ions present.

3 0

3 years ago