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3 years ago

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A cat jumps from a window 3 m from ground level. Its initial speed is 3 m/s, at 30° above the horizontal. Disregard air resistan

ce. a) How long does it stay in the air? b) How far from the building does it hit the ground? c) What is its velocity when it hits the ground?

1 answer:

Lelu [443]3 years ago

5 0

Answer:

a) $t=0.95s$

b) $x=2.46m$

c) $v=8.23m/s$

Explanation:

From the exercise we know that the initial height is 3m and the initial velocity is 3 m/s at 30º above the horizontal

a) To calculate how long does the cat stays in the air we need to know that at that moment y=0

$y=y_{o}+v_{oy}t+\frac{1}{2}gt^2$

$0=3+3sin(30)t-\frac{1}{2}(9.8)t^2$

Solving the quadratic equation for t:

$t=\frac{-b±\sqrt{b^2-4ac}}{2a}$

$a=-\frac{1}{2}(9.8)\\b=3sin(30)\\c=3$

$t=-0.64s$ or $t=0.95s$

Since time can not be negative, the cat stays in the air for 0.95s

b) The horizontal displacement is:

$x=v_{ox}t$

$x=(3cos(30)m/s)(0.95s)=2.46m$

c) To find its velocity when it hits the ground we need to analyze both x and y motion

$v_{x}=v_{ox}+at=3cos(30)=2.6m/s$

$v_{y}=v_{oy}-gt=3sin(30)m/s-9.8m/s^2(0.95s)=-7.81m/s$

So, v is:

$v=\sqrt{v_{x}^{2}+v_{y}^{2}}=\sqrt{(2.6m/s)^2+(-7.81m/s)^2}=8.23m/s$

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A cross-country skier slides horizontally along the snow and comes to rest after sliding a distance of 11 m. If the coefficient

Basile [38]

Answer:

v_o = 4.54 m/s

Explanation:

<u>Knowns </u>

From equation, the work done on an object by a constant force F is given by:

W = (F cos Ф)S (1)

Where S is the displacement and Ф is the angle between the force and the displacement.

From equation, the kinetic energy of an object of mass m moving with velocity v is given by:

K.E=1/2m*v^2 (2)

From The work- energy theorem , the net work done W on an object equals the difference between the initial and the find kinetic energy of that object:

W = K.E_f-K.E_o (3)

<u>Given </u>

The displacement that the sled undergoes before coming to rest is s = 11.0 m and the coefficient of the kinetic friction between the sled and the snow is μ_k = 0.020

<u>Calculations</u>

We know that the kinetic friction force is given by:

f_k=μ_k*N

And we can get the normal force N by applying Newton's second law to the sled along the vertical direction, where there is no acceleration along this direction, so we get:

∑F_y=N-mg

N=mg

Thus, the kinetic friction force is:

f_k = μ_k*N

Since the friction force is always acting in the opposite direction to the motion, the angle between the force and the displacement is Ф = 180°.

Now, we substitute f_k and Ф into equation (1), so we get the work done by the friction force:

W_f=(f_k*cos(180) s

=-μ_k*mg*s

Since the sled eventually comes to rest, K.E_f= 0 So, from equation (3), the net work done on the sled is:

W= -K.E_o

Since the kinetic friction force is the only force acting on the sled, so the net work on the sled is that of the kinetic friction force

W_f= -K.E_o

From equation (2), the work done by the friction force in terms of the initial speed is:

W_f=-1/2m*v^2

Now, we substitute for W_f= -μ_k*mg*s, and solving for v_o so we get:

-μ_k*mg*s = -1/2m*v^2

v_o = √ 2μ_kg*s

Finally, we plug our values for s and μ_k, so we get:

v_o = √2 x (0.020) x (9.8 m/s^2) x (11.0 m) = 4.54 m/s

v_o = 4.54 m/s

6 0

3 years ago

Read 2 more answers

Which of the following is true A. If the sum of the external forces on an object is zero, then the object must be in equilibrium

yanalaym [24]

Answer:

A. If the sum of the external forces on an object is zero, then the object must be in equilibrium

Explanation:

Equilibrium, in physics, the condition of a system when neither its state of motion nor its internal energy state tends to change with time.

For a single particle, equilibrium arises if the vector sum of all forces acting upon the particle is zero.

the object is at equilibrium, then the net force acting upon the object should be 0 Newton. Thus, if all the forces are added together as vectors, then the resultant force (the vector sum) should be 0 Newton.

There are three types of equilibrium: stable, unstable, and neutral

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3.7. A dog searching for a bone walks 3.50 m south, then 8.20 m at an angle 23.1 degrees north of east, and finally 15.0 m west.

andriy [413]

Answer:

Explanation:

We shall represent displacement of dog in vector form , in terms of i , j , i representing east and j representing north .

Dog travels 3.5 m south .

Displacement D₁ = - 3.5 j

then dog travels 8.2 m , 23.1 degree north of east

Displacement D₂ = 8.2 cos23.1 i + 8.2 sin23 j

D₂ = 8.2 cos23.1 i + 8.2 sin23.1 j

= 7.54 i + 3.22 j

Third displacement

D₃ = - 15i

Total displacement = D₁ + D₂ + D₃

= - 3.5 j + 7.54 i + 3.22 j -15i

= - 7.46 i - 0.28 j

Magnitude of displacement = √ ( 7.46² + .28²)

= √(55.65 + .08 )

= 7.46 m

b ) Direction of displacement

If Ф be angle , displacement makes with west direction

TanФ = .08 / 55.65 = .00143

Ф = .082 degree south of west or almost west .

From east , this angle = 180 + .082 = 180.082 , counterclockwise .

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2 years ago

Visible light passes through a diffraction grating that has 900 slits per centimeter, and the interference pattern is observed o

kobusy [5.1K]

Answer:

$\Delta \lambda=14.3\ nm$

Explanation:

It is given that,

The number of lines per unit length, N = 900 slits per cm

Distance between the formed pattern and the grating, l = 2.3 m

n the first-order spectrum, maxima for two different wavelengths are separated on the screen by 2.98 mm, $\Delta Y=2.98\ mm = 0.00298\ m$

Let d is the slit width of the grating,

$d=\dfrac{1}{N}$

$d=\dfrac{1}{900\ cm}$

$d=1.11\times 10^{-5}\ m$

For the first wavelength, the position of maxima is given by :

$y_1=\dfrac{L\lambda_1}{d}$

For the other wavelength, the position of maxima is given by :

$y_2=\dfrac{L\lambda_2}{d}$

So,

$\Delta \lambda=\dfrac{\Delta y d}{l}$

$\Delta \lambda=\dfrac{0.00298\times 1.11\times 10^{-5}}{2.3}$

$\Delta \lambda=1.43\times 10^{-8}\ m$

or

$\Delta \lambda=14.3\ nm$

So, the difference between these wavelengths is 14.3 nm. Hence, this is the required solution.

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padilas [110]

Answer:

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Explanation:

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