A jetliner flies west 2,000 miles from Chicago you San Francisco. It has an average speed of 635 mph relative to the air. What is the velocity of the jetliner relative to the earth of the wind is blowing at 160 mph from the west to the east?
475 mph, east
475 mph, west(my guess)
795 mph, west
795 mph, east
A hot air ballon rises vertically at a constant rate of 8 m/s. A second hot air balloon descends passed the first hot air balloon at rate of 12 m/s relative to the first hot air balloon. What is the velocity of the second hot air ballon relative to the ground?
4 m/s, Up
20 m/s. Up
4 m/s, down
20 m/s, down(my guess)
A hot air balloon rises vertically at a constant rate of 8 m/s. A second hot-air balloon moves past the first hot air balloon at 3 m/s downaward relative to the first hot air balloon. What is the velocity of the second hot air balloon relative to the ground?
5 m/s, up(my guess)
5 m/s, down
11 m/s, Up
13 m/s, down
To solve these problems, we need to understand the concept of velocity and how it combines with the effect of wind.
Question 1:
To find the velocity of the jetliner relative to the earth, we need to subtract the velocity of the wind from the velocity of the jetliner.
Given:
Velocity of the jetliner (relative to air) = 635 mph (west)
Velocity of the wind = 160 mph (east)
To find the velocity of the jetliner relative to the earth, subtract the velocity of the wind from the velocity of the jetliner:
Velocity of jetliner (relative to earth) = Velocity of jetliner (relative to air) - Velocity of wind
Substituting the given values:
Velocity of jetliner (relative to earth) = 635 mph (west) - 160 mph (east)
Since the velocities are in opposite directions (west and east), we subtract their magnitudes:
Velocity of jetliner (relative to earth) = 475 mph (west)
So, the answer to the first question is 475 mph, west.
Question 2:
To find the velocity of the second hot air balloon relative to the ground, we need to combine the vertical velocity of the first hot air balloon and the relative velocity between the two balloons.
Given:
Vertical velocity of the first hot air balloon = 8 m/s (up)
Relative velocity between the two balloons = 12 m/s (down)
To find the velocity of the second hot air balloon relative to the ground, we add the vertical velocity of the first balloon and the relative velocity between the two balloons:
Velocity of the second hot air balloon (relative to ground) = Vertical velocity of the first balloon + Relative velocity between the two balloons
Substituting the given values:
Velocity of the second hot air balloon (relative to ground) = 8 m/s (up) + 12 m/s (down)
Since the velocities are in opposite directions (up and down), we subtract their magnitudes:
Velocity of the second hot air balloon (relative to ground) = 4 m/s (down)
So, the answer to the second question is 4 m/s, down.
Question 3:
To find the velocity of the second hot air balloon relative to the ground, we again need to combine the vertical velocity of the first hot air balloon and the relative velocity between the two balloons.
Given:
Vertical velocity of the first hot air balloon = 8 m/s (up)
Relative velocity between the two balloons = 3 m/s (downward)
To find the velocity of the second hot air balloon relative to the ground, we add the vertical velocity of the first balloon and the relative velocity between the two balloons:
Velocity of the second hot air balloon (relative to ground) = Vertical velocity of the first balloon + Relative velocity between the two balloons
Substituting the given values:
Velocity of the second hot air balloon (relative to ground) = 8 m/s (up) + 3 m/s (downward)
Since the velocities are in opposite directions (up and downward), we subtract their magnitudes:
Velocity of the second hot air balloon (relative to ground) = 5 m/s (up)
So, the answer to the third question is 5 m/s, up.
To find the velocity of the jetliner relative to the earth when there is wind, we need to consider the vector addition of the airplane's velocity and the wind's velocity.
1. The velocity of the jetliner relative to the air is given as 635 mph west.
2. The wind blows at 160 mph from the west to the east.
To find the velocity of the jetliner relative to the earth, we need to subtract the wind's velocity from the velocity of the jetliner.
Given:
Velocity of the jetliner relative to the air = 635 mph, west
Velocity of the wind = 160 mph, east
To find the velocity of the jetliner relative to the earth, we subtract the wind's velocity from the jetliner's velocity:
Velocity of the jetliner relative to the earth = Velocity of the jetliner relative to the air - Velocity of the wind
Velocity of the jetliner relative to the earth = 635 mph, west - 160 mph, east
Velocity of the jetliner relative to the earth = 475 mph, west
Therefore, the correct answer is 475 mph, west.
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To find the velocity of the second hot air balloon relative to the ground, we need to consider the vector addition of the balloon's vertical velocity and the relative velocity between the two balloons.
Given:
Vertical velocity of the first hot air balloon = 8 m/s, up
Relative velocity of the second hot air balloon with respect to the first balloon = 12 m/s, down
To find the velocity of the second hot air balloon relative to the ground, we need to subtract its relative velocity with respect to the first balloon from the first balloon's vertical velocity.
Velocity of the second hot air balloon relative to the ground = Vertical velocity of the first hot air balloon - Relative velocity of the second hot air balloon with respect to the first balloon
Velocity of the second hot air balloon relative to the ground = 8 m/s, up - 12 m/s, down
Velocity of the second hot air balloon relative to the ground = 20 m/s, up
Therefore, the correct answer is 20 m/s, up.
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To find the velocity of the second hot air balloon relative to the ground, we need to consider the vector addition of the balloon's vertical velocity and the relative velocity between the two balloons.
Given:
Vertical velocity of the first hot air balloon = 8 m/s, up
Relative velocity of the second hot air balloon with respect to the first balloon = 3 m/s, downward
To find the velocity of the second hot air balloon relative to the ground, we need to add its relative velocity with respect to the first balloon to the first balloon's vertical velocity.
Velocity of the second hot air balloon relative to the ground = Vertical velocity of the first hot air balloon + Relative velocity of the second hot air balloon with respect to the first balloon
Velocity of the second hot air balloon relative to the ground = 8 m/s, up + 3 m/s, downward
Velocity of the second hot air balloon relative to the ground = 5 m/s, up
Therefore, the correct answer is 5 m/s, up.