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Vaselesa [24]
2 years ago
7

Unimpressed with your previous stunt, the director of the new James

Physics
1 answer:
Lyrx [107]2 years ago
8 0

Answer:

The minimum acceleration his partner will need in order to catch Bond before he hits the water is 25.688 meters per square second.

Explanation:

Let be the initial position of the sppedboat the reference location, James Bond jumps horizontally and experiments a parabolic motion, which consists in a horizontal motion at constant velocity and an vertical uniform accelerated motion due to gravity.

Speedboat must accelerate from rest and get Bond at right location and instant. Now we describe the appropriate equations of motion for James Bond and for the speedboat:

James Bond

x_{B} = x_{B,o} + v_{B,o,x} \cdot t

y_{B} = y_{B,o} + v_{B, o, y}\cdot t + \frac{1}{2}\cdot g \cdot t^{2}

Speedboat

x_{S} = x_{S,o}+v_{S,o}\cdot t + \frac{1}{2}\cdot a_{S}\cdot t^{2}

Where:

x_{B,o}, x_{S,o} - Initial horizontal positions for James Bond and the speedboat, measured in meters.

x_{B}, x_{S} - Current horizontal positions for James Bond and the speedboat, measured in meters.

v_{B,o,x}, v_{S,o} - Initial horizontal velocities of James Bond and the speedboat, measured in meters per second.

v_{B,o, y} - Initial vertical velocity of James Bond, measured in meters per second.

t - Time, measured in seconds.

g - Gravitational acceleration, measured in meters per square second.

a_{S} - Acceleration of the speedboat, measured in meters per square second.

We must observe the following conditions such as we may calculate the minimum acceleration of the speedboat:

1) x_{B} = x_{S}

2) y_{B} = 0\,m

Now, if we know that x_{B,o} = 60\,m, x_{S,o} = 0\,m, y_{B, o} = 18\,m, y_{B} = 0\,m, v_{B,o, x} = -6.7\,\frac{m}{s}, v_{S,o} = 0\,\frac{m}{s}, v_{B,o,y} = 0\,\frac{m}{s} and g = -9.807\,\frac{m}{s^{2}}, the resulting system of equations is:

60\,m +\left(-6.7\,\frac{m}{s} \right)\cdot t = 0\,m +\left(0\,\frac{m}{s} \right)\cdot t +\frac{1}{2}\cdot a_{S}\cdot t^{2}

\frac{1}{2}\cdot a_{S}\cdot t^{2} +\left(6.7\,\frac{m}{s} \right)\cdot t -60\,m = 0 (Eq. 1)

0\,m = 18\,m +\left(0\,\frac{m}{s} \right)\cdot t +\frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right) \cdot t^{2}

\frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right) \cdot t^{2}+18\,m = 0 (Eq. 2)

At first we get the time from (Eq. 2) by using the Quadratic Formula:

t_{1} \approx 1.916\,s and t_{2}\approx -1.916\,s

Only the first root is physically reasonable. (t\approx 1.916\,s)

Then, we substitute time in (Eq. 1) and clear the acceleration of the speedboat:

\frac{1}{2}\cdot a_{S}\cdot (1.916\,s)^{2} +\left(6.7\,\frac{m}{s} \right)\cdot (1.916\,s) -60\,m = 0

1.836\cdot a_{S}-47.163\,m = 0

a_{S} = 25.688\,\frac{m}{s^{2}}

The minimum acceleration his partner will need in order to catch Bond before he hits the water is 25.688 meters per square second.

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Answer:

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Explanation:

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Given :

The ball of a ballpoint pen is 0.5 mm in diameter and has an ASTM grain size of 12.

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Astronomers discover an exoplanet, a planet obriting a star other than the Sun, that has an orbital period of 3.27 Earth years i
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Answer:

  r = 3.787 10¹¹ m

Explanation:

We can solve this exercise using Newton's second law, where force is the force of universal attraction and centripetal acceleration

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The centripetal acceleration is given by

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For the case of an orbit the speed circulates (velocity module is constant), let's use the relationship

    v = d / t

The distance traveled Esla orbits, in a circle the distance is

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Time in time to complete the orbit, called period

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Let's replace

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Let's reduce the magnitudes to the SI system

     T = 3.27 and (365 d / 1 y) (24 h / 1 day) (3600s / 1h)

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Let's calculate

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      r = ∛ (21.44 10³⁵ / 39.478)

      r = ∛(0.0543087 10 36)

      r = 0.3787 10¹² m

      r = 3.787 10¹¹ m

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