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topjm [15]
3 years ago
11

why does the velocity in the horizontal direction remain constant while the velocity in the vertical direction changes?

Physics
1 answer:
Bond [772]3 years ago
8 0
The horizontal velocity<span> of a projectile is </span>constant<span> (a never </span>changing<span> in value), There is a </span>vertical<span>acceleration caused by gravity; its value is 9.8 m/s/s, down, The </span>vertical velocity<span> of a projectile </span>changes<span> by 9.8 m/s each second, The </span>horizontal<span> motion of a projectile is independent of its </span>vertical<span> motion.</span>
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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
0.
larisa [96]

Answer:21

Explanation:

4 0
2 years ago
Suppose you throw a ball vertically upward with a speed of 49 m/s. Neglecting air friction, what would be the height of the ball
vlabodo [156]

Answer:

78.4 m

Explanation:

Using newton's equation of motion,

S = ut + 1/2gt²......................... Equation 1

Where S = Height, t = time, u = initial velocity, g = acceleration due to gravity.

Note: Taking upward to be negative, and down ward positive

Given: u = 49 m/s, t = 2.0 s, g = -9.8 m/s²

Substitute into equation 1

S = 49(2) - 1/2(9.8)(2)²

S = 98 - 19.6

S = 78.4 m

Hence the height of the ball two seconds later = 78.4 m

6 0
3 years ago
Based on their locations on the periodic table, which two elements would you
Nat2105 [25]

Answer:

i think it would be B. Aluminum, Al and D. Boron, B

Explanation:

since they're both in group 13 and they forms a 3+ ion

6 0
3 years ago
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Acid rain is caused by human activity. Please select the best answer from the choices provided T F
olasank [31]

It is actually caused by the environment, so its false. :)

5 0
3 years ago
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