How is position time and motion related

Object A is moving due east, while object B is moving due north. They collide and stick together in a completely inelastic colli

serious [3.7K]

Answer:

pf = 198.8 kg*m/s

θ = 46.8º N of E.

Explanation:

Since total momentum is conserved, and momentum is a vector, the components of the momentum along two axes perpendicular each other must be conserved too.
If we call the positive x- axis to the W-E direction, and the positive y-axis to the S-N direction, we can write the following equation for the initial momentum along the x-axis:

$p_{ox} = p_{oAx} + p_{oBx} (1)$

We can do exactly the same for the initial momentum along the y-axis:

$p_{oy} = p_{oAy} + p_{oBy} (2)$

The final momentum along the x-axis, since the collision is inelastic and both objects stick together after the collision, can be written as follows:

$p_{fx} = (m_{A} + m_{B} ) * v_{fx} (3)$

We can repeat the process for the y-axis, as follows:

$p_{fy} = (m_{A} + m_{B} ) * v_{fy} (4)$

Since (1) is equal to (3), replacing for the givens, and since p₀Bₓ = 0, we can solve for vfₓ as follows:

$v_{fx} = \frac{p_{oAx}}{(m_{A}+ m_{B)}} = \frac{m_{A}*v_{oAx} }{(m_{A}+ m_{B)}} =\frac{17.0kg*8.00m/s}{46.0kg} = 2.96 m/s (5)$

In the same way, we can find the component of the final momentum along the y-axis, as follows:

$v_{fy} = \frac{p_{oBy}}{(m_{A}+ m_{B)}} = \frac{m_{B}*v_{oBy} }{(m_{A}+ m_{B)}} =\frac{29.0kg*5.00m/s}{46.0kg} = 3.15 m/s (6)$

With the values of vfx and vfy, we can find the magnitude of the final speed of the two-object system, applying the Pythagorean Theorem, as follows:

$v_{f} = \sqrt{v_{fx} ^{2} + v_{fy} ^{2}} = \sqrt{(2.96m/s)^{2} + (3.15m/s)^{2}} = 4.32 m/s (7)$

The magnitude of the final total momentum is just the product of the combined mass of both objects times the magnitude of the final speed:

$p_{f} = (m_{A} + m_{B})* v_{f} = 46 kg * 4.32 m/s = 198.8 kg*m/s (8)$

Finally, the angle that the final momentum vector makes with the positive x-axis, is the same that the final velocity vector makes with it.
We can find this angle applying the definition of tangent of an angle, as follows:

$tg \theta = \frac{v_{fy}}{v_{fx}} = \frac{3.15 m/s}{2.96m/s} = 1.06 (9)$

⇒ θ = tg⁻¹ (1.06) = 46.8º N of E

8 0

2 years ago

Calculate the power provided by a 12 volt car battery with a rating of 350 amperes.

mamaluj [8]

Answer:

Option D

4200 W

Explanation:

Power, P is also given as the product of voltage and current, expressed as P=VI

Here, P is power, V is voltage in the xircuit and I is current theough voltage.

Taking 12 V for voltage across and 350A for current across circuit then power will be

P=350*12=4200 W

Therefore, option D is correct.

8 0

2 years ago

A golf ball stays on the tee until the golf club hits it. Which of the following principles best describes why this occurs? Grou

givi [52]

Answer:

Newton's First Law of Motion.

Explanation:

Newton's first law of motion states that an object continues to stay in its state of rest, or of uniform motion, until acted upon by an external force.

So in the case of the golf ball here, the ball stays in its state of rest, on the tee, until the golf club hits it, i.e. , applies an external force on it.

Hence we can say that Newton's First Law of Motion is the principle which is most suitable for explaining this phenomenon.

7 0

3 years ago

When using the magnification equation, a value greater than 1 as the solution for M indicates that the image ? is larger than th

Nadusha1986 [10]

M= Height of image/height of the object

If, M>1, then height of image>height of object.

And therefore, image is larger than the object.

7 0

3 years ago

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According to Newton's law of universal gravitation, which statement is true?

valkas [14]

Answer:

Newton's law of gravitation, statement that any particle of matter in the universe attracts any other with a force varying directly as the product of the masses and inversely as the square of the distance between them.

6 0

3 years ago

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