To get to a concert in time, a harpsichordist has to drive 114 mi in 2.15 hours. If he drove at an average speed of 56.0 mi/h in a due west direction for the first 1.60 h, what must be his average speed if he is heading 31.3° south of west for the remaining 33 min? Give answer in mi/h. Do not enter unit.
Question
To get to a concert in time, a harpsichordist has to drive 114 mi in 2.15 hours. If he drove at an average speed of 56.0 mi/h in a due west direction for the first 1.60 h, what must be his average speed if he is heading 31.3° south of west for the remaining 33 min? Give answer in mi/h. Do not enter unit.
Solution
Step 1: Calculate the total distance covered in the first 1.60 hours.
The distance covered is given by the formula: Distance = Speed * Time
So, Distance = 56.0 mi/h * 1.60 h = 89.6 miles
Step 2: Calculate the remaining distance to be covered.
The total distance to be covered is 114 miles. So, the remaining distance is: 114 miles - 89.6 miles = 24.4 miles
Step 3: Convert the remaining time from minutes to hours.
33 minutes = 33/60 = 0.55 hours
Step 4: Calculate the average speed for the remaining distance.
The average speed is given by the formula: Speed = Distance / Time
So, Speed = 24.4 miles / 0.55 hours = 44.36 mi/h
Therefore, the harpsichordist must drive at an average speed of approximately 44.36 mi/h for the remaining 33 minutes.
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