To estimate the friend's average speed during the walk, we need to calculate the distance they walked and divide it by the time it took.
First, we can use trigonometry to find the distance the friend walked to reach the Phillips Hall door. Since the friend moved in a counterclockwise direction, we know that the angle formed by the line connecting the two doors and the line connecting the window and the Phillips Hall door is 63 degrees. Using the sine function, we can find the distance as follows:
Distance to Phillips Hall = 45 yards / sin(63 degrees) = 52.74 yards (approximately)
Next, we divide this distance by the time it took the friend to walk to find the average speed:
Average speed = Distance / Time = 52.74 yards / 48 seconds = 1.09875 yards per second (approximately)
Therefore, we would estimate the friend's average speed during the walk to be approximately 1.09875 yards per second.
From a window in Academy 7, one can observe the front door of Phillips Hall, which is about 45 yards away. A turn of the head through an angle of 63 degrees in a counterclockwise direction enables one to see the front door to Jeremiah Smith Hall which is about 65 yards away. If you spot a friend coming out of that door, and if that friend proceeds directly to the Phillips Hall door, making the trip in 48 seconds, what would you estimate to be your friend's average speed during the walk?
5 answers
use the cosine rule, the triangle is not a right triangle
Apologies for the confusion. You are correct that we cannot directly use the sine function since the triangle is not a right triangle.
To find the distance the friend walked, we can use the cosine rule. Let's define the angle formed by the line connecting the two doors, the line connecting the window and the Phillips Hall door as A, the distance from the window to the Phillips Hall door as x, and the distance from the window to the Jeremiah Smith Hall door as y.
According to the cosine rule, we have:
x^2 = 45^2 + 65^2 - 2 * 45 * 65 * cos(A)
Now, we know that the friend made the trip in 48 seconds, so their average speed can be calculated by dividing the total distance by the time:
Average speed = (x + y) / 48 seconds
To find y, we can use the sine rule. The angle formed by the line connecting the two doors, the line connecting the window and the Jeremiah Smith Hall door, and the angle A is supplementary to each other. So we have:
sin(A) = y / 65
Rearranging this equation, we get:
y = sin(A) * 65
Substituting this into the average speed equation, we have:
Average speed = (x + sin(A) * 65) / 48 seconds
To solve these equations, we need the value of angle A. Unfortunately, the problem statement does not provide this information, so we cannot make an accurate estimation of the friend's average speed without further data.
To find the distance the friend walked, we can use the cosine rule. Let's define the angle formed by the line connecting the two doors, the line connecting the window and the Phillips Hall door as A, the distance from the window to the Phillips Hall door as x, and the distance from the window to the Jeremiah Smith Hall door as y.
According to the cosine rule, we have:
x^2 = 45^2 + 65^2 - 2 * 45 * 65 * cos(A)
Now, we know that the friend made the trip in 48 seconds, so their average speed can be calculated by dividing the total distance by the time:
Average speed = (x + y) / 48 seconds
To find y, we can use the sine rule. The angle formed by the line connecting the two doors, the line connecting the window and the Jeremiah Smith Hall door, and the angle A is supplementary to each other. So we have:
sin(A) = y / 65
Rearranging this equation, we get:
y = sin(A) * 65
Substituting this into the average speed equation, we have:
Average speed = (x + sin(A) * 65) / 48 seconds
To solve these equations, we need the value of angle A. Unfortunately, the problem statement does not provide this information, so we cannot make an accurate estimation of the friend's average speed without further data.
A = 63
Apologies for missing that information. With A = 63 degrees, we can now proceed with the calculations.
Using the cosine rule, we have:
x^2 = 45^2 + 65^2 - 2 * 45 * 65 * cos(63 degrees)
x ≈ 78.95 yards
Now, let's find y using the sine rule:
sin(63 degrees) = y / 65
y ≈ sin(63 degrees) * 65 ≈ 57.27 yards
Average speed = (x + y) / 48 seconds
Average speed ≈ (78.95 + 57.27) / 48
Average speed ≈ 2.365 yards per second
Therefore, we would estimate your friend's average speed during the walk to be approximately 2.365 yards per second.
Using the cosine rule, we have:
x^2 = 45^2 + 65^2 - 2 * 45 * 65 * cos(63 degrees)
x ≈ 78.95 yards
Now, let's find y using the sine rule:
sin(63 degrees) = y / 65
y ≈ sin(63 degrees) * 65 ≈ 57.27 yards
Average speed = (x + y) / 48 seconds
Average speed ≈ (78.95 + 57.27) / 48
Average speed ≈ 2.365 yards per second
Therefore, we would estimate your friend's average speed during the walk to be approximately 2.365 yards per second.
2 answers