True or false? A system must contain more than one object.

A 33.0-kg child starting from rest slides down a water slide with a vertical height of 15.0 m. (Neglect friction.)

Temka [501]

This question involves the concept of the conservation of energy.

(a) The child's speed halfway will be "12.13 m/s".

(b) The child's speed three-fourth way will be "14.86 m/s".

(a)

Using the law of conservation of energy:

Potential Energy Lost = Kinetic Energy Gained

$mgh = \frac{1}{2}mv^2\\\\2gh = v^2\\\\v = \sqrt{2gh}$

where,

v = speed = ?

g = acceleration due to gravity = 9.81 m/s²

h = height lost = halfway = height/2 = 15 m/2 = 7.5 m

Therefore,

$v = \sqrt{(2)(9.81\ m/s^2)(7.5\ m)}$

v = 12.13 m/s

(b)

Using the law of conservation of energy:

Potential Energy Lost = Kinetic Energy Gained

$mgh = \frac{1}{2}mv^2\\\\2gh = v^2\\\\v = \sqrt{2gh}$

where,

v = speed = ?

g = acceleration due to gravity = 9.81 m/s²

h = height lost = three-fourth way down = $\frac{3}{4}height = \frac{3}{4}(15\ m) = 11.25\ m$

Therefore,

$v = \sqrt{(2)(9.81\ m/s^2)(11.25\ m)}$

v = 14.86 m/s

Learn more about the law of conservation of energy here:

brainly.com/question/20971995?referrer=searchResults

The attached picture shows the law of conservation of energy.

7 0

3 years ago

Determine the projection (magnitude and sign), or component, of vector v1 along the direction of vector v2. Your answer could be

professor190 [17]

Answer:

- 1.07 ft

Explanation:

V1 = (-5, 7, 2)

V2 = (3, 1, 2)

Projection of v1 along v2, we use the following formula

=\frac{\overrightarrow{V1}.\overrightarrow{V2}}{V2}

So, the dot product of V1 and V2 is = - 5 (3) + 7 (1) + 2 (2) = -15 + 7 + 4 = -4

The magnitude of vector V2 is given by

= $\sqrt{3^{2}+1^{2}+2^{2}}=3.74$

So, the projection of V1 along V2 = - 4 / 3.74 = - 1.07 ft

Thus, the projection of V1 along V2 is - 1.07 ft.

so we need to find the direction of v2

7 0

4 years ago

A beam of electrons moving in the x-direction enters a region where a uniform 208-G magnetic field points in the y-direction. Th

GREYUIT [131]

Answer:

$1.26\cdot 10^7 m/s$

Explanation:

When a charged particle moves perpendicularly to a magnetic field, the force it experiences is:

$F=qvB$

where

q is the charge

v is its velocity

B is the strength of the magnetic field

Moreover, the force acts in a direction perpendicular to the motion of the charge, so it acts as a centripetal force; therefore we can write:

$qvB=m\frac{v^2}{r}$

where

m is the mass of the particle

r is the radius of the orbit of the particle

The equation can be re-arranges as

$v=\frac{qBr}{m}$

where in this problem we have:

$q=1.6\cdot 10^{-19}C$ is the magnitude of the charge of the electron

$B=208 G=208\cdot 10^{-4}T$ is the strength of the magnetic field

The beam penetrates 3.45 mm into the field region: therefore, this is the radius of the orbit,

$r=3.45 mm = 3.45\cdot 10^{-3} m$

$m=9.11\cdot 10^{-31} kg$ is the mass of the electron

So, the electron's speed is

$v=\frac{(1.6\cdot 10^{-19})(208\cdot 10^{-4})(3.45\cdot 10^{-3})}{9.11\cdot 10^{-31}}=1.26\cdot 10^7 m/s$

6 0

3 years ago

Why are SI units helpful for describing objects? A. They are the standard used by scientists worldwide. B. They are more accurat

Ganezh [65]

They are the standard system used by scientists worldwide, and
officially by almost all nations of the world. So if you describe a
measurement in terms of SI units, there's less chance that you'll
need to explain the measurement to anyone who reads it ...
most scientists and common people worldwide will understand
what your number means.

7 0

3 years ago

A transverse sinusoidal wave on a string has a period T= 25.0ms and travels in the negative x direction with a speed of 30.0 m/s

aleksandrvk [35]

The wave is equation with the given conditions is y = 0.02 cos ( 0 )

Given data

period T= 25.0ms

speed of 30.0 m/s

t = 0

x = 0

transverse position of 2.00cm

speed of 2.0 m/s = v

<h3>writing the wave function </h3>

frequency f = 1 / T

f = 1 / 25

f = 0.04Hz

Angular velocity = ω = 2 * pi * f

ω = 2 * pi * 0.04

ω = 0.251

wave number K = ω / v

k = 0.251 / 2

k = 0.126

The wave equation

y = A cos ( kx + ωt )

this is equivalent to

y = 0.02 cos ( 0.126 * 0 + 0.251 * 0 )

y = 0.02 cos ( 0 )

Read more on wave equation here: brainly.com/question/28167443

#SPJ4

6 0

1 year ago