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2 years ago

Police officer at rest at the side of the highway

1 answer:

4 0

Let's take the police officers starting position as our origin, that is Sp(t0) = Ss(t0) = 0, and, since we know the police officers starts from a standstill, Vp(t0) = 0 and Vs(t0) = 62km/h

For the first part of the pursuit, during the officers acceleration:

Sp(t) = Sp(t0) + Vp(t0)*t + (3/2)*t^2

Sp(t) = 1.5*t^2

Vp(t) = 3*t

We need to know how much time transpires during this first bit, that is until the officers speed is 72 km/h or 20m/s, and we can find that out by using Vp(t):

Vp(t1) = 20 = 3*t1

t1 = 3.33... s

We now look at how much space each of them covers during this time:

Sp(t1) = 1.5*(t1)^2 = 16.66... m

Ss(t1) = Vs*t1 = (62/3.6)*(3.33...) = 57.41 m

For the second part of the pursuit we will take the officers position as our origin:

Sp(t) = 20*t

Ss(t) = (57.41 - 16.66) + (17.22...)*t

Now we just need to equate Sp(t) to Ss(t):

20*t = (40.75) + (17.22...)*t

t = 40.75/(2.77...) = 14.67 s

But we need to add the time in the first part of the pursuit to the time we just found:

14.67 + 3.33 = 18s

The pursuit lasts 18 seconds.

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You and your dog are walking along a pond. Your dog looks into the still water and is startled to see its reflection. Which phen

attashe74 [19]

You just identified the image as a "reflection", so it's a pretty good bet that
the phenomenon involves reflection somehow.

Your dog can see his reflection in a mirror inside the house just as easily
as in the surface of the pond. My dogs do it all the time. The phenomenon
doesn't require water.

It's reflection of light waves.

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2 years ago

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A 0.110 kg cube of ice (frozen water) is floating in glycerine. The glycerine is in a tall cylinder that has inside radius 3.70

Sonbull [250]

Answer:

the distance by which the height of the liquid in the cylinder change after the ice gets melted = 0.528 cm

Explanation:

The change in volume of glycerin when the ice cube is placed on the surface of the glycerin can be represented as:

$V = \frac{m}{ \rho}$

Given that ;

the mass of the ice cube (m) = 0.11 kg = 0.110 × 10³ g

density of the glycerine ( $\rho$ ) = 1.260 kg/L = 1.260 g/cm³

Then:

V = $\frac{0.110*10^3 \ g}{1.260 \ g/cm^3}$

V = $0.0873*10^3 \ cm^3 (\frac{1L}{10^3 cm^3})$

V = 0.0873 L

Now;Initially the volume of the glycerin before the ice cube starts to melt is:

$V_1 = V_i + V\\\\V_1 = V_i+ 0.0873 \ L$

However; the volume of the water produced by the 0.11 kg ice cube = $0.11*10^3 \ cm^3$

The expression for change in the volume of glycerin after the ice cube starts to melt is as follows:

$V_2 = V_i + V"$

replacing $V"$ with $0.11*10^3 \ cm^3$ ; we have:

$V_2 = V_i (0.11*10^3 \ cm^3 )(\frac{1 \ L }{10^3 \ cm^3})$

$V_2 = V_i + 0.11 \ L$

The overall total change in the volume of the glycerin is illustrated as:

$V_f = V_2 - V_1$

Now; from the foregoing ; lets replace the respective value of $V_2$ and $V_1$ in the above equation ; we have;

$V_f = (V_i + 0.11 \ L) - (V_i + \ 00873 \ L)\\ \\V_f = 0.11 L - 0.0873 \ L\\\\V_f = 0.0227 \ L$

The formula usually known to be the volume of a cylinder is :

$V = \pi r ^2 h$

For the question ; we will have:

$V_f = \pi r ^2 h$

making h the subject of the formula ; we have:

$h = \frac{V_f}{\pi r^2}$

replacing 0.0227 L for $V_f$ and the given value of radius which is = 3.70 cm; we have:

$h = \frac{0.0227 \ L ( \frac{10^3 \ cm^3}{1\ L})}{\pi * (3.70 cm)^2}$

$h = \frac{22.7 \ cm^3}{\pi * (3.70 cm)^2}\\\\h = 0.528 \ \ cm$

Thus ; the distance by which the height of the liquid in the cylinder change after the ice gets melted = 0.528 cm

8 0

2 years ago

An object with a mass m slides down a rough 37° inclined plane where the coefficient of kinetic friction is 0.20. If the plane i

hodyreva [135]

Answer: 9.312 m/s

Explanation:

The friction force (opposite to the motion) is Fa = μ*m*g*cos(α) with μ = kinetic friction. The force that makes the motion is

F = m*g*sin(α).

The Newton's law gives:

F - Fa = m*a

m*g*sin(α) - μ*m*g*cos(α) = m*a

g*sin(α) - μ*g*cos(α) = a so a = 4.335 m/s²

It's a uniformly accelerated motion:

Space

S = 0.5*a*t²

10 = 0.5*a*t²

=> t = 2.148 s

Velocity

V = a*t = 9.312 m/s.

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2 years ago

Which muscle disorder does donna’s doctor diagnose? donna is suffering from leg pain in which the calf muscles contract involunt

Kay [80]

Donna's doctor must have diagnosed her with muscle cramps. With the given symptoms above, it is likely that she is experiencing muscle cramps. Muscle cramps most likely happen when the individual experiencing it is lack of fluid intake, causing the muscles to tighten causing pain and for the muscle to contract involuntarily.

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2 years ago

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A spring has a spring constant of 48 N/m. The end of the spring hangs 8 m above the ground. How much weight can be placed on the

Setler79 [48]

The answer is 96 N .....................................

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2 years ago

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