While riding in a hot air balloon, which is steadily descending at a speed of 1.39 m/s, you accidentally drop your cell phone.

(a) After 4.00 s, what is the speed of the cell phone?

(b) How far is the cell phone below the balloon after this time?
d = m

(c) What are your answers to parts (a) and (b) if the balloon is rising steadily at 1.39 m/s?
v =

The analysis is the same as in parts (a) and (b), only now the balloon is moving upward. How will that affect the distance between the balloon and phone at the later time? m/s
d = m

(a) To find the speed of the cell phone after 4.00 seconds, we need to consider two factors: the initial speed of the cell phone and the acceleration due to gravity.

The initial speed of the cell phone is 0 m/s because it was dropped from rest.

The acceleration due to gravity is approximately 9.8 m/s^2 and acts downward.

Therefore, after 4.00 seconds, the speed of the cell phone can be calculated using the formula:

Speed = Initial Speed + (Acceleration x Time)

Speed = 0 + (9.8 x 4.00)

Speed = 0 + 39.2

Speed = 39.2 m/s

So, after 4.00 seconds, the speed of the cell phone is 39.2 m/s.

(b) To find how far the cell phone is below the balloon after 4.00 seconds, we can use the formula for distance traveled under constant acceleration:

Distance = Initial Speed x Time + (0.5 x Acceleration x Time^2)

Since the initial speed of the cell phone is 0 m/s, the equation simplifies to:

Distance = (0.5 x Acceleration x Time^2)

Distance = (0.5 x 9.8 x 4.00^2)

Distance = 0.5 x 9.8 x 16.00

Distance = 78.4 meters

So, after 4.00 seconds, the cell phone is 78.4 meters below the balloon.

(c) If the balloon is rising steadily at 1.39 m/s, the analysis is the same as in parts (a) and (b), but the initial speed is now considered positive.

(a) After 4.00 seconds, the speed of the cell phone would be:

Speed = Initial Speed + (Acceleration x Time)
Speed = 1.39 + (9.8 x 4.00)
Speed = 1.39 + 39.2
Speed = 40.59 m/s

So, after 4.00 seconds, the speed of the cell phone would be 40.59 m/s.

(b) To find how far the cell phone is below the balloon after 4.00 seconds in this scenario, we can again use the formula:

Distance = (0.5 x Acceleration x Time^2)
Distance = (0.5 x 9.8 x 4.00^2)
Distance = 0.5 x 9.8 x 16.00
Distance = 78.4 meters

Therefore, after 4.00 seconds, the cell phone would still be 78.4 meters below the balloon.

(c) The fact that the balloon is moving upward does not affect the distance between the balloon and the phone at the later time. The acceleration due to gravity acts downward, and the balloon's upward motion does not impact this acceleration. Thus, the distance between the balloon and phone remains unchanged at 78.4 meters.

To solve this problem, we need to use the equations of motion and consider the initial velocity, final velocity, time, and distance.

(a) After 4.00 seconds, we need to find the speed of the cell phone.
Since the hot air balloon is descending at a steady speed, the initial velocity of the cell phone is the same as the balloon's velocity, which is 1.39 m/s downward. The time is given as 4.00 s.
The final velocity can be calculated using the equation:

Final velocity = Initial velocity + (acceleration * time)

In this case, there is no acceleration, so the equation becomes:

Final velocity = Initial velocity

Thus, after 4.00 seconds, the speed of the cell phone will be 1.39 m/s downward.

(b) To find how far the cell phone is below the balloon after 4.00 seconds, we can use the equation:

Distance = Initial velocity * time + (1/2) * acceleration * time^2

Since the initial velocity and acceleration are both downwards, we can substitute their values into the equation:

Distance = (1.39 m/s) * (4.00 s) + (1/2) * (0) * (4.00 s)^2

Note that the acceleration is zero since the balloon is descending at a steady speed. Simplifying the equation, we get:

Distance = (1.39 m/s) * (4.00 s)

Therefore, after 4.00 seconds, the cell phone will be 5.56 meters below the balloon.

(c) If the balloon is rising steadily at 1.39 m/s, we need to re-evaluate the answers to parts (a) and (b).

(a) The speed of the cell phone after 4.00 seconds will be the difference between the velocity of the balloon and the velocity of the cell phone.
Velocity of the cell phone = Velocity of the balloon - Velocity of the phone
Velocity of the cell phone = 1.39 m/s (upward)

(b) The distance between the balloon and the cell phone after 4.00 seconds will be the same as part (b), with the sign flipped due to the opposite direction of motion. The distance will be:

Distance = -(1.39 m/s) * (4.00 s)

Therefore, after 4.00 seconds, the cell phone will be 5.56 meters above the balloon.

Note: In part (c), since the balloon is rising, the distance between the balloon and the cell phone will decrease over time.

10m/s

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