d1 = 45m/h * 1h = 45mi @ 0 deg.
d2 = 45m/h * 0.5h = 22.5mi @ 45deg.
X = hor. = 45 + 22.5cos45 = 60.91mi.
Y = ver. = 22.5sin45 = 15.91mi.
d^2 = X^2 + Y^2,
d^2 = (60.91)^2 + (15.91)^2 = 3963.16,
d = 62.95mi.
d2 = 45m/h * 0.5h = 22.5mi @ 45deg.
X = hor. = 45 + 22.5cos45 = 60.91mi.
Y = ver. = 22.5sin45 = 15.91mi.
d^2 = X^2 + Y^2,
d^2 = (60.91)^2 + (15.91)^2 = 3963.16,
d = 62.95mi.
First, let's find the distance traveled east. The car traveled for 1 hour at a speed of 48 mi/h. Using the formula distance = speed Γ time, we can calculate:
Distance traveled east = 48 mi/h Γ 1 h = 48 mi
Next, let's find the distance traveled northeast. The car traveled for 30 minutes, which is half an hour, at a speed of 48 mi/h. Again, using the formula distance = speed Γ time, we can calculate:
Distance traveled northeast = 48 mi/h Γ 0.5 h = 24 mi
Now, we can use these two distances to calculate the total distance from the car's starting position. We can create a right-angled triangle with the distance traveled east and the distance traveled northeast as the two legs.
Using the Pythagorean theorem, the hypotenuse of the triangle is equal to the total distance from the car's starting position. The formula for the hypotenuse is:
Hypotenuse = β(legβ^2 + legβ^2)
Hypotenuse = β(48 mi^2 + 24 mi^2)
Hypotenuse = β(2304 mi^2 + 576 mi^2)
Hypotenuse = β2880 mi^2
Hypotenuse β 53.67 mi
Therefore, the car is approximately 53.67 miles away from its starting position.
First, let's find the distance traveled east. The car traveled east for 1 hour at a constant speed of 48 mi/h. So, the distance traveled east is:
Distance east = speed * time = 48 mi/h * 1 h = 48 miles.
Next, let's find the distance traveled northeast. The car traveled northeast for 30 minutes. To find the distance, we need to calculate the horizontal and vertical components of this distance.
The horizontal component is the distance traveled east while going northeast. We can use trigonometry to find this distance. Since the car is traveling at a 45-degree angle (northeast), the horizontal component is the same as the vertical component. So, the horizontal component is:
Horizontal component = 48 miles * cos(45 degrees) = 48 miles * 0.7071 = 33.94 miles.
The vertical component is the distance traveled north while going northeast. Again, using trigonometry, we can calculate this distance. Since the car is traveling at a 45-degree angle (northeast), the vertical component is the same as the horizontal component. So, the vertical component is:
Vertical component = 48 miles * sin(45 degrees) = 48 miles * 0.7071 = 33.94 miles.
Now, let's calculate the total distance from the starting position. We can use the Pythagorean theorem to find this distance. The horizontal and vertical components form a right triangle with the total distance as the hypotenuse. So, the total distance is:
Total distance = β(Horizontal component^2 + Vertical component^2) = β((33.94 miles)^2 + (33.94 miles)^2) = β(1152.96 mi^2 + 1152.96 mi^2) = β2305.92 mi^2 = 47.99 miles.
Rounded to 2 decimal places, the car is approximately 48.00 miles from its starting position.