Assume a hockey player accelerates from 0 ft/s to 24 ft/s over a period of 2

The coordinates of a bird flying in the xy plane are given by x(t)=αt and y(t)=3.0m−βt2, where α=2.4m/s and β=1.2m/s2. Calculate

yuradex [85]

The derivative of the function space as a function of time is equal to a function of speed as a function of time.

$x(t)=2.4t \\ \frac{x(t)}{t}=t \\ v_{x}(t)=t \\ \\ y(t)=3-1.2\times t^2 \\ \frac{y(t)}{t}=1.2\times2t \\ v_{y}(t)=2.4t$

The velocity vector is given by the vector sum of the velocities of both axes.

$v_{R}^2(t)=v_{x}^2(t)+v_{y}^2(t) \\ v_{R}^2(t)=(t)^2+(2.4t)^2 \\ \boxed {v_R(t)=2.6t}$

If you notice any mistake in my english, please let me know, because I am not native.

4 0

4 years ago

Read 2 more answers

Vectors A and B lie in the xy ‑plane. Vector A has a magnitude of 17.1 and is at an angle of 150.5∘ counterclockwise from the +x

IRINA_888 [86]

Answer:

A = -14.87 i ^ + 8.42 j ^ + 0 k ^

B = -25.41 i ^ -12.0 j ^ + 0 k ^

Explanation:

For this exercise let's use trigonometry by decomposing to vectors

vector A

module 17.1 with an angle of 150.5 counterclockwise.

Sin 150.5 = $A_{y}$ / A

cos 150.5 = Ax / A

A_{y} = A sin 150.5 = 17.1 sin 150.5

Aₓ = A cos 1505 = 172 cos 150.5

A_{y} = 8,420

Aₓ = -14.870

the vector is

A = -14.87 i ^ + 8.42 j ^ + 0 k ^

Vector B

$B_{y}$ = 28.1 sin 205.3

Bₓ = 28.1 cos 205.3

B_{y} = -12.009

Bₓ = -25.405

the vector is

B = -25.41 i ^ -12.0 j ^ + 0 k ^

5 0

3 years ago

A fan uses 7A when connected to a 110V line. If electric power costs 10 cents per kilowatt-hour in this location, what is the co

Anna007 [38]

Power = current x voltage

So the power is 7 x 110 = 770 W = 0.77kW

0.77 x 13 = 10.01 kWh

10.01 x 10 cents = 100.1 cents (is this 1 dollar? Idk I use a different currency)

6 0

4 years ago

The combined focal length of two thin lens is 24 cm and the focal length of one converging lens is 8

qwelly [4]

Answer: f = -12 cm

Explanation: <u>Combined</u> <u>lenses</u> is an array of simple lenses with a common axis. The combination is useful for correction of optical aberrations which cannot be corrected by simple lenses.

When two lenses are in contact and are thin, focal lengths are related as:

$\frac{1}{F} =\frac{1}{f_{1}} +\frac{1}{f_{2}}$

If there is a distance between the lenses, the focal length will be:

$\frac{1}{F} =\frac{1}{f_{1}} +\frac{1}{f_{2}} -\frac{d}{f_{1}f_{2}}$

Since the lenses in the question above are thin and in contact, the focal length of one of them will be:

$\frac{1}{F} =\frac{1}{f_{1}} +\frac{1}{f_{2}}$

$\frac{1}{f_{2}} =\frac{1}{f_{1}} -\frac{1}{F}$

$\frac{1}{f_{2}} =\frac{1}{8} -\frac{1}{24}$

$\frac{1}{f_{2}} =\frac{-2}{24}$

$f_{2}=$ -12

The focal length of the other lens is -12 cm, with the negative sign meaning it's a converging lens.

7 0

3 years ago

How would the mathematical model change if the direction that the object traveled was reversed

victus00 [196]

A line that is falling towards the x axis represents an object that is negatively accelerating, or slowing down. When the line hits the x axis, the object has stopped moving. If the graph continues below the x axis, the object has changed direction and is moving backwards at increasing velocity.

7 0

3 years ago