Question

A balloon drifts 50 m toward the east in 6 s; then the wind suddenly changes, and the balloon flies 30 m toward the west in the next 5 s. What was the average speed and velocity during the first 6 seconds? What was the average speed and velocity during the next 5 seconds? What was the average speed and velocity for the whole trip? Show work for all.

Answer 1

The average speed and velocity for the first 6 seconds were 8.33 m/s and 8.33 m/s east, respectively. For the next 5 seconds, the average speed was 6 m/s, and the average velocity was -6 m/s east. The entire trip had an average speed of 7.27 m/s and average velocity of 1.82 m/s east.

Step-by-step explanation:

The question asks to calculate the average speed and velocity of a balloon over different intervals and then for the entire journey. to calculate average speed, you divide the total distance traveled by the total time taken, regardless of direction. Velocity, however, is a vector quantity, so it does take direction into account and is calculated by dividing the total displacement by the total time.

First 6 seconds:

Average speed = Total distance ÷ Time = 50 m ÷ 6 s = 8.33 m/s

Average velocity = Displacement ÷ Time = 50 m east ÷ 6 s = 8.33 m/s east

Next 5 seconds:

Average speed = Total distance ÷ Time = 30 m ÷ 5 s = 6 m/s

Average velocity = Displacement ÷ Time = 30 m west ÷ 5 s = -6 m/s east (west is considered negative)

Whole trip:

Total distance = 50 m + 30 m = 80 m

Total displacement = 50 m - 30 m = 20 m east

Total time = 6 s + 5 s = 11 s

Average speed = Total distance ÷ Total time = 80 m ÷ 11 s = 7.27 m/s

Average velocity = Total displacement ÷ Total time = 20 m east ÷ 11 s = 1.82 m/s east