A camel sets out to cross the desert, which is 49.8 km wide in the north-south direction. The camel walks at the uniform speed 2.64 km/hr along a straight line in the direction 50.1� north of East (only the camel knows why he chose that particular direction).
How long will it take the camel to cross the desert?
Answer in units of hr
49.8/sin(50.1)= 64.91km
t= 64.91/2.64= 24.59hr
To find out how long it will take the camel to cross the desert, we need to determine the distance it needs to travel.
Given that the desert is 49.8 km wide in the north-south direction, we can use the Pythagorean theorem to calculate the total distance the camel needs to walk. The Pythagorean theorem states that the square of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the other two sides (a and b).
In this case, we have a right triangle with the north-south distance as one side (a) and the east-west distance as the other side (b). The distance the camel needs to cross the desert is the hypotenuse (c) of this right triangle.
To find the north-south distance, we can use the cosine function:
cos(θ) = adjacent/hypotenuse
Where θ is the angle of the direction (50.1 degrees north of East) and adjacent is the north-south distance.
So, cos(50.1) = adjacent/c.
Rearranging the equation, we get:
adjacent = cos(50.1) * c
Since we know that c is the width of the desert (49.8 km), we can substitute that value into the equation:
adjacent = cos(50.1) * 49.8 km
Using a calculator, we find that cos(50.1) ≈ 0.6428. Therefore,
adjacent ≈ 0.6428 * 49.8 km
adjacent ≈ 32.0244 km
So, the north-south distance the camel needs to travel is approximately 32.0244 km.
Now, we can use the speed of the camel to calculate the time it will take to cross the desert. The camel walks at a uniform speed of 2.64 km/hr.
Dividing the north-south distance by the speed, we get:
time = distance/speed
time = 32.0244 km / 2.64 km/hr
Using a calculator, we find that the time is approximately 12.15 hours.
Therefore, it will take the camel approximately 12.15 hours to cross the desert.