Physics, 31.01.2021 06:00 Frankie103947

9) A rock is projected upwards from the surface of the moon at time t = 0.0 s with a velocity of 30 m/s (the acceleration due to gravity at the surface of the moon is -1.62 m/s2. The rock rises, then falls and strikes the ground. Consider all quantities as positive in the upward direction. What is the velocity during accent at 180 m above the surface? At time t = 10 s, what is the height of the rock from the ground?

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Answer from: kingo7

a) The velocity of the rock during ascent at 180 meters above the surface is approximately 17.799 meters per second.

b) The height of the rock from the ground is 219 meters from the ground.

Explanation:

a) The rock experiments a free fall, in which this element is projected upwards, decelerated until rest is reached and then it falls down. Please notice that free fall is a case of uniformly accelerated motion, in which object is accelerated by gravity. The velocity of the rock is described by the following kinematic equation:

$v = \sqrt{v_{o}^{2}+2\cdot a\cdot \Delta s}$ (1)

Where:

$v_{o}$ - Initial velocity, measured in meters per second.

- Final velocity, measured in meters per second.

- Gravitational acceleration, measured in meters per square second.

$\Delta s$ - Travelled distance, measured in meters.

If we know that $v_{o} = 30\,\frac{m}{s}$ , $a = -1.62\,\frac{m}{s^{2}}$ and $\Delta s = 180\,m$ , then the velocity during ascent at 180 meters is:

$v =\sqrt{\left(30\,\frac{m}{s} \right)^{2}+2\cdot \left(-1.62\,\frac{m}{s^{2}}\right)\cdot (180\,m) }$

$v \approx 17.799\,\frac{m}{s}$

The velocity of the rock during ascent at 180 meters above the surface is approximately 17.799 meters per second.

b) The height of the rock is calculated from this kinematic formula:

$s = s_{o}+v_{o}\cdot t +\frac{1}{2}\cdot a \cdot t^{2}$ (2)

Where:

$s_{o}$ - Initial position of the rock, measured in meters.

- Final position of the rock, measured in meters.

$v_{o}$ - Initial velocity of the rock, measured in meters per second.

- Time, measured in seconds.

- Acceleration, measured in meters per square second.

If we know that $s_{o} = 0\,m$ , $v_{o} = 30\,\frac{m}{s}$ , $t = 10\,s$ and $a = -1.62\,\frac{m}{s^{2}}$ , then the height of the rock from the ground is:

$s = 0\,m + \left(30\,\frac{m}{s} \right)\cdot (10\,s)+\frac{1}{2}\cdot \left(-1.62\,\frac{m}{s^{2}} \right)\cdot (10\,s)^{2}$

$s = 219\,m$

The height of the rock from the ground is 219 meters from the ground.

Answer from: Quest

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm. the wire diameter is d = 0.9 mm. the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2) in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

Answer from: Quest

Nucleus for question ome

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