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3 years ago

A cyclist makes the following trip along two vectors; he travels 9km to the north and then travels 6km to the east

Physics

1 answer:

elena-14-01-66 [18.8K]3 years ago

6 0

Answer:

Final distance from the origin: 10.82 km. the vector points as shown in the attached image.

Angle with respect to the east: $56.31^o$

Explanation:

Please refer to the attached image. The cyclist's trip is indicated with the green arrows (9 km to the north followed by 6 km to the east.

So his final position is at the tip of this last vector, and indicated by the orange vector drawn form the point where the trip starts to the cyclist's final location.

We observe that this orange vector is in fact the hypotenuse of a right angle triangle, and we can estimate the distance from the origin by the Pythagorean theorem:

$d=\sqrt{9^2+6^2} \\d=\sqrt{81+36} \\d=\sqrt{117} \\d=10.82 \,\,km$

Notice that this is NOT the actual number of km that the cyclist pedaled to reach the final point.

Now, to find the value of the angle $\theta$ , we need to use trigonometry, and in particular the tangent function gives us the ratio between the side of the triangle "opposite" to the angle, divided the side "adjacent" to the angle:

$tan(\theta)=\frac{opp}{adj} \\tan(\theta)=\frac{9}{6}\\tan(\theta)=\frac{3}{2}\\$

Now we can find the value of the angle by using the arctan function:

$tan(\theta)=\frac{3}{2} \\\theta=arctan(\frac{3}{2} )\\\theta= 56.31^o$

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ustapha Jones is speeding on the interstate in his Ferrari at 231km/hr when he passes a police car at rest . If the cop accelera

Lena [83]

Answer:

461 km/h

Explanation:

In order to solve this problem we must first sketch a drawing of what the situation looks like so we can better visualize it. (See attached picture).

We have two situations there, the first one is Mustapha's car that is traveling at a constant speed of 231km/hr.

The second situation is the police that is accelerating from rest until he reaches Mustapha. (We are going to suppose the acceleration is constant and that he will not stop accelerating until he reaches Mustapha). He has an acceleration of 15m/ $s^{2}$ .

We want to find what the final velocity of the police is at the time he reaches Mustapha. From this we can imply that the displacement x will be the same for both particles.

So let's model the first situation.

The displacement of Mustapha can be found by using the following equation:

$V_{M}=\frac{x}{t}$

when solving the equation for the displacement x we get that it will be:

$x=V_{M}t$

Now let's model the displacement of the cop. Since the cop has a constant acceleration, we can model his displacement with the following formula.

$x=V_{0}t+\frac{1}{2}at^{2}$

Since the initial velocity of the cop is zero, we can get rid of that part of the equation leaving us with:

$x=\frac{1}{2}at^{2}$

We can now set both equations equal to each other so we get:

$\frac{1}{2}at^{2}=V_{M}t$

When solving this for t, we get that:

$t=\frac{2V_{M}}{a}$ (let's call this equation 1)

Now, we know the cop has constant acceleration, so we can model it with the following formula too:

$a=\frac{V_{f}-V_{0}}{t}$

since the initial velocity of the cop is zero, we can get rid of that here too, so we get the following formula:

$a=\frac{V_{f}}{t}$

when solving for the final velocity, we get that:

$V_{f}=at$ (let's call this equation 2)

when substituting equation 1 into equation 2 we get:

$V_{f}=a(\frac{2V_{M}}{a})$

we can now cancel a leaving us with:

$V_{f}=2V_{M}$

This tells us that the final velocity of the cop will not depend on his acceleration. (This is only if the acceleration is constant all the time) So we get that the final velocity of the cop is:

$V_{f}=2(231km/hr)$

$V_{f}=461km/hr$

which is our answer.

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3 years ago

ANSWER ASAP PLEASEEE Kendra wonders what would happen if the oceans did not exist on Earth. Based on her understanding of the oc

Cloud [144]

Answer:

that there would be more clouds.

Explanation:

one of the cycles is precipitation. without water there would be no rain and clouds are what causes the rain to come down

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3 years ago

A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at eye level) by t

marishachu [46]

At the highest point of the trajectory the vertical component will have its zero velocity, and the descent caused by the force of gravity will begin.

Since the ball is thrown with a certain speed, the vertical component reaches its highest point (upwards), until returning to the receiver who will receive the ball with the same vertical component but in the opposite direction (downwards).

Therefore the vertical component will have its highest value at launch.