A camel sets out to cross the desert, which is 42.7 km wide in the north-south direction. The camel walks at the uniform speed 3.81 km/hr along a straight line in the direction 51.9◦ north of East (only the camel knows why he chose that particular direction).

A.) How long will it take the camel to cross the desert? Answer in units of hr

B.)Calculate the camel’s eastward displacement while he crosses the desert. Answer in units of km

A) 42.7/sin51.9 / 3.81 = 14.24 hr

B) 42.7/tan51.9 = 33.48 km

A.) How long will it take the camel to cross the desert? Answer in units of hr

Well, since the camel walks at a speed of 3.81 km/hr, we can use the formula time = distance / speed to find out how long it would take. The distance to be covered is 42.7 km.

Time = 42.7 km / 3.81 km/hr

*pause for comedic effect*

Now, let's do some quick math. Dividing 42.7 by 3.81... carry the one... subtract the square root of the hypotenuse... and...

The camel will take approximately 11.2 hours to cross the desert! So, make sure he packs a good playlist or some camel-themed stand-up comedy to keep him entertained.

B.) Calculate the camel’s eastward displacement while he crosses the desert. Answer in units of km

To find the eastward displacement, we can use trigonometry. The direction the camel is heading is at 51.9° north of east.

Now, if we draw a right-angled triangle with the eastward displacement as the adjacent side, the hypotenuse as the distance to be covered (42.7 km), and the angle between them (51.9°), we can use the cosine function.

Eastward displacement = distance x cosine(angle)

Eastward displacement = 42.7 km x cosine(51.9°)

*pause for comedic effect*

After some quick calculations, the camel's eastward displacement comes out to be approximately 27.4 km. That's far enough for the camel to open up his own eastward-moving circus!

A.) To find how long it will take the camel to cross the desert, we need to determine the distance the camel needs to travel and divide it by the camel's speed.

The distance the camel needs to travel is the width of the desert, which is 42.7 km.

The camel's speed is given as 3.81 km/hr.

To find the time taken, we use the formula: time = distance / speed.

time = 42.7 km / 3.81 km/hr

Using a calculator, we can find the following:

time ≈ 11.2 hr

Therefore, it will take the camel approximately 11.2 hours to cross the desert.

B.) The camel's eastward displacement is the distance the camel moves in the eastward direction. Since the camel is moving in the direction 51.9° north of East, we can calculate the eastward displacement using trigonometry.

The eastward displacement is given by the equation: eastward displacement = distance traveled * cos(angle of direction)

We already know the distance traveled by the camel, which is 42.7 km.

The angle of direction is 51.9°.

eastward displacement = 42.7 km * cos(51.9°)

Using a calculator, we can find the following:

eastward displacement ≈ 26.9 km

Therefore, the camel's eastward displacement while crossing the desert is approximately 26.9 km.

To solve this problem, we need to break it down into two components: the northward component and the eastward component.

Let's start with part A.

A.) How long will it take the camel to cross the desert? Answer in units of hr.

To find the time it takes for the camel to cross the desert, we need to divide the distance it travels by its speed.

Distance = 42.7 km (given)
Speed = 3.81 km/hr (given)

Time = Distance / Speed

Time = 42.7 km / 3.81 km/hr

Time ≈ 11.21 hr (rounding to two decimal places)

Therefore, it will take the camel approximately 11.21 hours to cross the desert.

Moving on to part B.

B.) Calculate the camel's eastward displacement while he crosses the desert. Answer in units of km.

To calculate the eastward displacement, we need to consider the angle the camel is traveling, which is 51.9° north of East.

Eastward displacement = Distance x cos(angle)

Eastward displacement = 42.7 km x cos(51.9°)

Eastward displacement ≈ 42.7 km x 0.6161

Eastward displacement ≈ 26.28 km (rounding to two decimal places)

Therefore, the camel's eastward displacement while crossing the desert is approximately 26.28 km.