Final answer:
Horton's total displacement is 1 mile.
Step-by-step explanation:
To calculate Horton's total displacement, we need to consider his initial velocity, the time it takes for him to change direction, and his final velocity. First, let's convert Horton's initial velocity from miles per hour to meters per second. Since 1 mile is approximately equal to 1609 meters, we can convert 5.00 mi/hr to meters per second by multiplying it by (1609 m/1 mi) and dividing by (3600 s/1 hr). This gives us an initial velocity of approximately 2.24 m/s to the East.
Next, let's calculate the change in velocity. Horton accelerates at a rate of 1.50 m/s^2 West for 1 minute, which is equivalent to 60 seconds. Therefore, the change in velocity is given by Δv = 1.50 m/s^2 * 60 s = 90 m/s to the West.
Finally, we can calculate Horton's final velocity by subtracting the change in velocity from the initial velocity. Final velocity = Initial velocity - Change in velocity = 2.24 m/s - 90 m/s = -87.76 m/s to the West.
To find the total displacement, we can use the equation: displacement = (1/2) * (initial velocity + final velocity) * time. Since Horton changed direction, the displacement is given by: displacement = (1/2) * (2.24 m/s - 87.76 m/s) * 60 s = -3156 m/s * 60 s = -189,360 m.
Since the displacement is negative, it means Horton ended up 189,360 meters to the West of his starting point. To convert this to miles, we divide by (1609 m/1 mi), which gives us a total displacement of approximately -117.8 miles. However, we are only interested in the magnitude of the displacement, so the final answer is approximately 117.8 miles. Therefore, the correct answer is D. 1.00 mile.