A sailboat travels 45km eastward at a speed of 20km/hr. The wind then drops, and the boat continues due east with a speed of 15km/hr for 25km.
a.How long did it take the boat to travel 55km?
b. What was the average velocity for the trip?
a. T = d1/V1 + d2/V2 = 45/20 + 10/15 = 2.92 Hours.
b. T1 = d1/V1 = 45/20 = 2.25 Hours.
T2 = d2/V2 = 25/15 = 1.67 Hours.
Vavg=(d1+d2)/(T1+T2)=(45+25)/(2.25+1.67)
= 17.86 km/h.
To find the time taken by the boat to travel 55km, we can split the journey into two parts: the first part where it travels 45km at a speed of 20km/hr, and the second part where it travels 25km at a speed of 15km/hr.
a. Time taken for the first part:
Distance = Speed × Time
45km = 20km/hr × Time
To find Time, we can rearrange the equation:
Time = Distance / Speed
Time = 45km / 20km/hr
Time = 2.25 hours
Time taken for the second part:
Distance = Speed × Time
25km = 15km/hr × Time
Similarly,
Time = 25km / 15km/hr
Time = 1.67 hours
Total time taken to travel 55km = Time taken for the first part + Time taken for the second part
Total time taken = 2.25 hours + 1.67 hours
Total time taken = 3.92 hours (rounded to two decimal places)
b. Average velocity for the trip can be calculated by finding the total displacement and dividing it by the total time taken.
For the first part, the boat travels 45km eastwards, so the displacement is 45km towards the east.
For the second part, the boat travels 25km due east, so the displacement is also 25km towards the east.
Total displacement = Displacement for the first part + Displacement for the second part
Total displacement = 45km + 25km
Total displacement = 70km (towards the east)
Average velocity = Displacement / Time taken
Average velocity = 70km / 3.92 hours
Average velocity ≈ 17.86 km/hr (rounded to two decimal places)
Therefore, the boat took approximately 3.92 hours to travel 55km, and the average velocity for the trip was approximately 17.86 km/hr.