Question

In: Physics

jogger travels a route that has two parts. The first is a displacement of 2.75 km...

jogger travels a route that has two parts. The first is a displacement of 2.75 km due south, and the second involves a displacement that points due east. The resultant displacement has a magnitude of 4.25 km. (a) What is the magnitude of , and (b) what is the direction of    as a positive angle relative to due south? Suppose that - had a magnitude of 4.25 km. (c) What then would be the magnitude of , and (d) what is the direction of - relative to due south?

a.) number ___ units ___

b. number____ units _____

c. number____ units_____

d. number____ units_____

Solutions

Expert Solution

| 2.75 km
|
|______ b

I'm assuming the jogger is jogging km, not nautical miles. I suppose Jesus could jog nautical miles. Anywho

This is a right triangle and you know the hypotenuse and one leg, and want the other leg and then the angle between the vertical and the hypotenuse.

hyp^2 = 2.75^2 + b^2
4.25^2 = 2.75^2 + b^2
18.0625 = 7.5625 + b^2
b = 3.24 km

The angle can be found through any of the reverse trig functions.

x = arcsin(3.24/4.25)
x = arcos(2.75/4.25)
x = arctan(3.24/2.75)

x = 49.67 degrees east of south

Subtracting a vector is the same as adding a negative vector. In this case, it would mean running west instead of east. The magnitude won't change. It will still be 3.24 km. The angle between the vector 4.25 km and the vector 2.75 km is now 49.67 degrees WEST of south. However, they want a vector relating to due west, so we have to find the complement.

90 - 49.67 = 40.33

So 40.33 degrees south of west.

a.) 3.24 km

b.) 49.67 degrees east of south

c.) 3.24 km

d.) 40.33 degrees south of west


Related Solutions

A jogger travels a route that has two parts. The first is a displacement of 2.90...
A jogger travels a route that has two parts. The first is a displacement of 2.90 km due south, and the second involves a displacement that points due east. The resultant displacement + has a magnitude of 3.90 km. (a) What is the magnitude of , and (b) what is the direction of + as a positive angle relative to due south? Suppose that - had a magnitude of 3.90 km. (c) What then would be the magnitude of ,...
A pilot flies her route in two straight-line segments. The displacement vector A for the first...
A pilot flies her route in two straight-line segments. The displacement vector A for the first segment has a magnitude of 235 km and a direction 30.0o north of east. The displacement vector B for the second segment has a magnitude of 173 km and a direction due west. The resultant displacement vector is R = A + B and makes an angle θ with the direction due east. Using the component method, find (a) the magnitude of R and...
A ship of 5000 tonnes displacement has KG 4.2m and KM 4.5m, and is listed 5...
A ship of 5000 tonnes displacement has KG 4.2m and KM 4.5m, and is listed 5 degrees to port. Assuming that the KM remains constant, find the final list if 80 tonnes of bunkers are loaded in No. 2 starboard tank whose centre of gravity is 1 metre above the keel and 4 metres out from the centreline. book name ship stability for masters and mates sixth edition
Anna Laura rides her bike. First she travels 3.5 km due east, then she takes a...
Anna Laura rides her bike. First she travels 3.5 km due east, then she takes a left turn and travels 2.5 km due north. Draw a graph illustrating the motion; be sure to choose a valid coordinate system and indicate the length scale of your axes. Draw the displacement vector x. Write the vector x include the magnitude and the direction; the direction can be an angle relative to one of your axes.
A horizontally projected beam of protons travels at 55 km/s into the space between two horizontal,...
A horizontally projected beam of protons travels at 55 km/s into the space between two horizontal, parallel plates. The plates are separated by 7.4 cm, and they are 12 cm long. There is a uniform electric field between the plates of unknown strength. The beam enters the region exactly midway (vertically) between the plates and exits the region 7.2 microns closer to the lower plate. If it were a beam of electrons instead, everything else being the same, at what...
An automobile has a vertical radio antenna 1.10 m long. The automobile travels at70.0 km/h on...
An automobile has a vertical radio antenna 1.10 m long. The automobile travels at70.0 km/h on a horizontal road where the Earth's magnetic field is 50.0 µT, directed toward the north and downwards at an angle of 65.0° below the horizontal. (a) Specify the direction the automobile should move in order to generate the maximum motional emf in the antenna, with the top of the antenna positive relative to the bottom. (b) Calculate the magnitude of this induced emf.
An automobile has a vertical radio antenna 1.40 m long. The automobile travels at 56.0 km/h...
An automobile has a vertical radio antenna 1.40 m long. The automobile travels at 56.0 km/h on a horizontal road where Earth's magnetic field is 50.0 µT, directed toward the north and downward at an angle of 65.0° below the horizontal. Calculate the magnitude of this induced emf. ...........MV
Your assignment this week has two parts: First, you will create a timeline or infographic to...
Your assignment this week has two parts: First, you will create a timeline or infographic to address the following questions: Research and provide examples or comparisons that demonstrate these changes over time from each of the categories: Print, Radio/Music, Cinema, Television, and the Internet. Include images of each artifact. How have these various forms of communication have evolved since they were first introduced? (Give a “before” and “after”) Second, you will write a mini-statement answering the following question. In 300-500...
This question has two parts. Please answer both, thank you! Part A.) On the first day...
This question has two parts. Please answer both, thank you! Part A.) On the first day of the fiscal year, a company issues a $8,200,000, 9%, 9-year bond that pays semiannual interest of $369,000 ($8,200,000 × 9% × ½), receiving cash of $6,868,206. Journalize the first interest payment and the amortization of the related bond discount. Round to the nearest dollar. If an amount box does not require an entry, leave it blank. Interest Expense Discount on Bonds Payable Cash...
Question 1 The binomial formula has two parts. The first part of the binomial formula calculates...
Question 1 The binomial formula has two parts. The first part of the binomial formula calculates the number of combinations of X successes. The second part of the binomial formula calculates the probability associated with the combination of success and failures. If N=4 and X=2, and p = .5, what is that probability from the second part of the formula? Group of answer choices .0625 .5 .3750 .1563 Question 2 Normal Distribution Problem. The birth weight is of newborn babies...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT