Motion is the process of changing __

A rifle fires a 2.10 x 10^-2 kg pellet straight upward, because the pellet rests on a compressed spring when the trigger is is p

yKpoI14uk [10]

m = mass of pellet = 2.10 x 10⁻² kg

x = compression of spring at the time launch = 9.10 x 10⁻² m

h = height gained by the pellet above the initial position = 6.10 m

k = spring constant

using conservation of energy

spring potential energy = gravitational potential energy of pellet

(0.5) k x² = m g h

inserting the values

(0.5) k (9.10 x 10⁻²)² = (2.10 x 10⁻²) (9.8) (6.10)

k = 303.2 N/m

4 0

3 years ago

A boat crossing a 153.0 m wide river is directed so that it will cross the river as quickly as possible. The boat has a speed of

Lynna [10]

We have the relation

$\vec v_{B \mid E} = \vec v_{B \mid R} + \vec v_{R \mid E}$

where $v_{A \mid B}$ denotes the velocity of a body A relative to another body B; here I use B for boat, E for Earth, and R for river.

We're given speeds

$v_{B \mid R} = 5.10 \dfrac{\rm m}{\rm s}$

$v_{R \mid E} = 3.70 \dfrac{\rm m}{\rm s}$

Let's assume the river flows South-to-North, so that

$\vec v_{R \mid E} = v_{R \mid E} \, \vec\jmath$

and let $-90^\circ < \theta < 90^\circ$ be the angle made by the boat relative to East (i.e. -90° corresponds to due South, 0° to due East, and +90° to due North), so that

$\vec v_{B \mid R} = v_{B \mid R} \left(\cos(\theta) \,\vec\imath + \sin(\theta) \, \vec\jmath\right)$

Then the velocity of the boat relative to the Earth is

$\vec v_{B\mid E} = v_{B \mid R} \cos(\theta) \, \vec\imath + \left(v_{B \mid R} \sin(\theta) + v_{R \mid E}\right) \,\vec\jmath$

The crossing is 153.0 m wide, so that for some time $t$ we have

$153.0\,\mathrm m = v_{B\mid R} \cos(\theta) t \implies t = \dfrac{153.0\,\rm m}{\left(5.10\frac{\rm m}{\rm s}\right) \cos(\theta)} = 30.0 \sec(\theta) \, \mathrm s$

which is minimized when $\theta=0^\circ$ so the crossing takes the minimum 30.0 s when the boat is pointing due East.

It follows that

$\vec v_{B \mid E} = v_{B \mid R} \,\vec\imath + \vec v_{R \mid E} \,\vec\jmath \\\\ \implies v_{B \mid E} = \sqrt{\left(5.10\dfrac{\rm m}{\rm s}\right)^2 + \left(3.70\dfrac{\rm m}{\rm s}\right)^2} \approx 6.30 \dfrac{\rm m}{\rm s}$

The boat's position $\vec x$ at time $t$ is

$\vec x = \vec v_{B\mid E} t$

so that after 30.0 s, the boat's final position on the other side of the river is

$\vec x(30.0\,\mathrm s) = (153\,\mathrm m) \,\vec\imath + (111\,\mathrm m)\,\vec\jmath$

and the boat would have traveled a total distance of

$\|\vec x(30.0\,\mathrm s)\| = \sqrt{(153\,\mathrm m)^2 + (111\,\mathrm m)^2} \approx \boxed{189\,\mathrm m}$

3 0

2 years ago

two forces 3N and 4N act on a body in a direction due north and due East respectively calculate their equivalent

Lostsunrise [7]

Two forces 3N and 4N act on a body in a direction due north From East, the equilibrant's angle is given by $\theta=\tan ^{-1} \frac{3}{4}=36.8^{\circ}$ .

<h3>What are equilibrium and resultant force?</h3>

The equilibrium force is the balanced force when the net force acting is zero and is the exact opposite of the consequent force. The resultant force is one single force replaced by numerous forces.

<h3>Briefing:</h3>

3N and 4N are the two forces pulling on a body.

The forces work along the North and the East, which are perpendicular to one another.

The resultant of the forces, which is provided by the equilibrant force,

R = √(3)²+(4)²

R = 5N

From East, the equilibrant's angle is given by

$\theta=\tan ^{-1} \frac{3}{4}=36.8^{\circ}$

To know more about equilibrium force visit:

brainly.com/question/12582625

#SPJ9

6 0

1 year ago

Suppose you drop a 10-pound weight and a 5-pound weight on the Moon, both from the same height at the same time. What will happe

Murljashka [212]

Answer:

Both will hit the ground at the same time.

3 0

2 years ago

Which of the following properties of a sound wave determines its loudness (or intensity): wavelength, speed, amplitude, or frequ

lara31 [8.8K]

Answer: Amplitude

Explanation: The intensity or loudness of a sound depends upon the extent to which the sounding body vibrates (i.e the amplitude of vibration).

Loudness is measured in units called decibels and amplitude in metre

4 0

3 years ago

Motion is the process of changing ___