The height is h = 17 10⁶ meters above the surface of Mars. To determine this, we apply Newton's second law according to the universal law of gravitation, represented by F = m a. The centripetal acceleration a is expressed as v² / r. Applying the gravitational force we have G m M / r² = m v² / r. Given that the speed of the object remains constant, we derive v from d / t, where d is the circumference and t is the orbital period. Substituting gives us d = 2π r and v = 2π r / T. Replacing these values leads to the equation G M / r² = (4π² r² / T) / r, so r³ = G M T² / 4π². Converting time into SI units, T = 24.66 h converts to 88776 seconds. Ultimately, the computed value of r is 2,045 10⁶ m, and after subtracting Mars’ radius of 3.39 10⁶ m, we find the height h to be 17 10⁶ m.
The astronaut's speed is described in the sentence. The astronaut moves at a rate of 10 meters each minute. To clarify: speed is defined as distance divided by time and is characterized solely by its magnitude, not its direction. Hence, the 10 meters per minute reflects this. We lack information about the astronaut's directional movement. In contrast to speed, velocity incorporates direction as well; for instance, a velocity of 10m/s due west provides a directional context. Consequently, without specified direction, the value indicated is merely speed.
<span>We will apply the momentum-impulse theorem here. The total momentum along the x-direction is defined as p_(f) = p_(1) + p_(2) + p_(3) = 0.
Therefore, p_(1x) = m1v1 = 0.2 * 2 = 0.4. Additionally, p_(2x) = m2v2 = 0 and p_(3x) = m3v3 = 0.1 *v3, where v3 represents the unknown speed and m3 signifies the mass of the third object, which has an unspecified velocity.
In the same way, for the particle of 235g, the y-component of the total momentum is described with p_(fy) = p_(1y) + p_(2y) + p_(3y) = 0.
Thus, p_(1y) = 0, p_(2y) = m2v2 = 0.235 * 1.5 = 0.3525 and p_(3y) = m3v3 = 0.1 * v3, where m3 is the mass of the third piece.
Consequently, p_(fx) = p_(1x) + p_(2x) + p_(3x) = 0.4 + 0.1v3; yielding v3 = 0.4/-0.1 = - 4.
Similarly, p_(fy) = 0.3525 + 0.1v3; thus v3 = - 0.3525/0.1 = -3.525.
Therefore, the x-component of the speed of the third piece is v_3x = -4 and the y-component is v_3y = 3.525.
The overall speed is calculated as follows: resultant = âš (-4)^2 + (-3.525)^2 = 5.335</span>
Answer:
10000 V
0.00225988700565 m²
Explanation:
E = Electric field = 
d = Distance = 2.5 mm
Q = Charge = 80 nC
= Permittivity of free space = 
The potential difference is calculated as
The potential difference across the plates amounts to 10000 V
Area is determined by
The area of each plate measures 0.00225988700565 m²
Capacitance is determined by
The capacitance is
The radius of the moon's orbit is calculated as R = 7.715 x 10⁷ m, and the moon's orbital period is T = 14.48 hr. The given orbital speed of the moon is v = 9.3 x 10³ m/s, with Neptune's mass being M = 1.0 x 10²⁶ Kg. The moon's orbital velocity can be expressed using the formula. Therefore, by squaring the equation and resolving for r + h, we calculate: R = GM / v². Upon substituting in, we find R to be 7.715 x 10⁷ m. The relation for the moon's orbital period yields T = 2π/ω and simplistically, T = 2πR/v, where ω = v/r. Following this, we compute T, leading to the conclusion: T = 14.48 hr.
