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1 year ago

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An object travels back and forth along a straight line. its velocity, in centimeters per second, is given by the function v(t) =

equals 13 sine (startfraction pi over 45 endfraction t), where t is time in seconds. what is the maximum velocity of the object? 0 cm/s 13 cm/s 26 cm/s 90 cm/s

1 answer:

algol131 year ago

8 0

The correct option for the maximum velocity of the object is the option

13 cm/s.

<h3>What are Functions?</h3>

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

The reason for the selection is as follows:

The known parameters of the motion of the vehicle are:

The type motion of the vehicle = Repetitive back and forth

The path of the motion of the object = Along a straight line

The function that gives the velocity in centimeters per second (cm/s) is given as follows;

v(t) = 13. sin(π/45 . t)

Where;

t = The time in seconds (a set of the input variables of the function)

v(t) = The velocity of the object (the output variables of the function)

The maximum output value of the sine function = 1, therefore;

sin(π/45 . t) = 1

The units of the of the function is cm/s

Therefore, the maximum velocity of the object is 13 cm/s

learn more about functions go to -

brainly.com/question/6561461

#SPJ4

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A ship maneuvers to within 2.46×10³ m of an island’s 1.80 × 10³ m high mountain peak and fires a projectile at an enemy ship 6.1

Nesterboy [21]

Answer:

The distance close to the peak is 597.4 m.

Explanation:

Given that,

Distance of the first ship from the mountain $d=2.46\times10^{3}\ m$

Height of island $h=1.80\times10^{3}\ m$

Distance of the enemy ship from the mountain $d'=6.10\times10^{2}\ m$

Initial velocity $v=2.55\times10^{2}\ m/s$

Angle = 74.9°

We need to calculate the horizontal component of initial velocity

Using formula of horizontal component

$v_{x}=v\cos\theta$

Put the value into the formula

$v_{x}=2.55\times10^{2}\cos74.9$

$v_{x}=66.42\ m/s$

We need to calculate the vertical component of initial velocity

Using formula of vertical component

$v_{y}=v\sin\theta$

Put the value into the formula

$v_{y}=2.55\times10^{2}\sin74.9$

$v_{y}=246.19\ m/s$

We need to calculate the time

Using formula of time

$t=\dfrac{d}{v_{x}}$

$t=\dfrac{2.46\times10^{3}}{66.42}$

$t=37.03\ sec$

We need to calculate the height of the shell on reaching the mountain

Using equation of motion

$H= v_{y}t-\dfrac{1}{2}gt^2$

Put the value in the equation

$H=246.19\times37.03-\dfrac{1}{2}\times9.8\times(37.03)^2$

$H=2397.4\ m$

We need to calculate the distance close to the peak

Using formula of distance

$H'=H-h$

Put the value into the formula

$H'=2397.4-1800$

$H'=597.4\ m$

Hence, The distance close to the peak is 597.4 m.

6 0

3 years ago

In some circumstances, it is useful to look at the linear velocity of a point on the blade. The linear velocity of a point in un

mihalych1998 [28]

Answer:

$v=wr$

Explanation:

<u>Tangent and Angular Velocities</u>

In the uniform circular motion, an object describes the same angles in the same times. If $\theta$ is the angle formed by the trajectory of the object in a time t, then its angular velocity is

$\displaystyle w=\frac{\theta}{t}$

if $\theta$ is expressed in radians and t in seconds the units of w is rad/s. If the circular motion is uniform, the object forms an angle $2\theta$ in 2t, or $3\theta$ in 3t, etc. Thus the angular velocity is constant.

The magnitude of the tangent or linear velocity is computed as the ratio between the arc length and the time taken to travel that distance:

$\displaystyle v=\frac{\theta r}{t}$

Replacing the formula for w, we have

$\boxed{ v=wr}$

4 0

3 years ago

7. These temperatures were recorded in Pasadena for a week in April. 87 85 80 78 83 86 90 Find each of these. (a) Mean (e) Range

slega [8]

Answer:

a) Mean = 84.14

b) Median = 85

c) Mode = no mode (since there is no variable that appears more than once in this dataset)

d) Midrange = 84

e) Range = 12

f) Variance = 14.69

g) Standard deviation = 3.83

Explanation:

The raw data to be processed is

87 85 80 78 83 86 90

a) Mean = (Σx)/N

The mean is the sum of variables divided by the number of variables

x = each variable

N = number of variables = 7

Mean = (87+85+80+78+83+86+90)/7

Mean = 84.14

b) Median is the number in the middle of the dataset when the variables are arranged in ascending or descending order.

Arranging the data in ascending order

78, 80, 83, 85, 86, 87, 90

The number in the middle is the 4th number = 85

Median = 85

c) Mode is the variable that occurs the most in a distribution.

For this question, all of the variables occur only once, with no variable occurring more than once. Hence, there is no mode for this dataset.

d) Midrange is the arithmetic mean of the highest and lowest number in the dataset.

Mathematically,

Midrange = (Highest + Lowest)/2

Midrange = (90 + 78)/2

Midrange = 84

e) Range is the difference the highest and the lowest numbers in a dataset.

Range = 90 - 78 = 12

f) Variance is an average of the squared deviations from the mean.

Mathematically,

Variance = [Σ(x - xbar)²/N]

xbar = mean

Σ(x - xbar)² = (78 - 84.14)² + (80 - 84.14)² + (83 - 84.14)² + (85 - 84.14)² + (86 - 84.14)² + (87 - 84.14)² + (90 - 84.14)² = 102.8572

Variance = (102.8572)/7

Variance = 14.69

g) Standard deviation = √(variance)

Standard deviation = √(14.69)

Standard deviation = 3.83

Hope this Helps!!!

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3 years ago

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Alex17521 [72]

The range of a projectile can be found directly using:
R = (v²sin2∅) / g
v = √((98 x 9.81)/(sin(90)))
v = 31.0 m/s

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3 years ago

To get to your baseball game, you had to drive 2 kilometers north, then 5 kilometers west, and finally 2 kilometers south. What

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Answer is C. 5 km west

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