A hot air balloon is moving vertically upwards at a velocity of 3m/s. A sandbag is dropped when the balloon reaches 150m. How long does the sandbag take to reach the ground and what is the maximum height it reaches?
Answers
This is a perfect opportunity to stuff all that data into the general equation for the height of an object that has some initial height, and some initial velocity, when it is dropped into free fall.
H(t) = (H₀) + (v₀ T) + (1/2 a T²)
Height at any time 'T' after the drop =
(initial height) +
(initial velocity) x (T) +
(1/2) x (acceleration) x (T²) .
For the balloon problem ...
-- We have both directions involved here, so we have to define them:
Upward = the positive direction
Initial height = +150 m
Initial velocity = + 3 m/s
Downward = the negative direction
Acceleration (of gravity) = -9.8 m/s²
Height when the bag hits the ground = 0 .
H(t) = (H₀) + (v₀ T) + (1/2 a T²)
0 = (150m) + (3m/s T) + (1/2 x -9.8 m/s² x T²)
-4.9 T² + 3T + 150 = 0
Use the quadratic equation:
T = (-1/9.8) [ -3 plus or minus √(9 + 2940) ]
= (-1/9.8) [ -3 plus or minus 54.305 ]
= (-1/9.8) [ 51.305 or -57.305 ]
T = -5.235 seconds or 5.847 seconds .
(The first solution means that the path of the sandbag is part of
the same path that it would have had if it were launched from the
ground 5.235 seconds before it was actually dropped from balloon
while ascending.)
Concerning the maximum height ... I don't know right now any other
easy way to do that part without differentiating the big equation.
So I hope you've been introduced to a little bit of calculus.
H(t) = (H₀) + (v₀ T) + (1/2 a T²)
H'(t) = v₀ + a T
The extremes of 'H' (height) correspond to points where h'(t) = 0 .
Set v₀ + a T = 0
+3 - 9.8 T = 0
Add 9.8 to each side: 3 = 9.8 T
Divide each side by 9.8 : T = 0.306 second
That's the time after the drop when the bag reaches its max altitude.
Oh gosh ! I could have found that without differentiating.
- The bag is released while moving UP at 3 m/s .
- Gravity adds 9.8 m/s of downward speed to that every second.
So the bag reaches the top of its arc, runs out of gas, and starts
falling, after
(3 / 9.8) = 0.306 second .
At the beginning of that time, it's moving up at 3 m/s.
At the end of that time, it's moving with zero vertical speed).
Average speed during that 0.306 second = (1/2) (3 + 0) = 1.5 m/s .
Distance climbed during that time = (average speed) x (time)
= (1.5 m/s) x (0.306 sec)
= 0.459 meter (hardly any at all)
But it was already up there at 150 m when it was released.
It climbs an additional 0.459 meter, topping out at 150.459 m,
then turns and begins to plummet earthward, where it plummets
to its ultimate final 'plop' precisely 5.847 seconds after its release.
We can only hope and pray that there's nobody standing at
Ground Zero at the instant of the plop.
I would indeed be remiss if were to neglect, in conclusion,
to express my profound gratitude for the bounty of 5 points
that I shall reap from this work. The moldy crust and tepid
cloudy water have been delicious, and will not soon be forgotten.
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The baseball will undergo 16 revolutions on its way to home plate.
Explanation:
As the parameters which are given are speed at which the baseball is thrown, (v = 90 mi/h) and the distance between the home plate and the ball thrown is 60 ft. Also the spin is said to 1950 rev/min, it indicates that the ball will undergo 1950 revolution in every single minute. So in order to determine the number of revolutions the baseball will make in its way to home plate, we have to first determine the time taken for the baseball to reach its home plate with the given speed.
As we know that speed can be obtained by the ratio of distance with time, in the present case, we know the speed and distance, then time can be obtained by ratio of distance with speed.
At first, we have to convert the speed from mi/h to ft/min
1 mi/hr = 5280/ 60 ft/min = 88 ft/min.
Then, Time = Distance/Speed = 60/(90×80)=60/7200=8.33 × 10⁻³ min
Since the ball undergoes 1950 revolutions in 1 min, then in 8.33 × 10⁻³ min, the number of revolutions will be 1950×8.33 × 10⁻³ = 16 rev
Thus, the baseball will undergo 16 revolutions on its way to home plate.
Answers
Answers
the rate of the plane?
Answers
the plane is on a average of 100km a hour
Answer:
on average, the plane is traveling at 100km per hour, so i think the rate is 100:1
Explanation:
Answers
The following cause that is notconsidered in the formation of a Dust Bowl is the lack of farmers in Oklahoma.The answer is letter B. in fact, the number of farmers increases due to thehigh grain prices of Worl War I that encourages farmers to plow millions ofacres of natural grass to plant wheat.
Answer:
With the advent of pesticides, minerals in the ground were leached.
Explanation:
got it right on odyssey
Answers
Answer:
r= 3.2 cm
Explanation:
Given that
I= 8.7 A
B= 5.4 x 10⁻⁵ T
μo=1.25664 x 10⁻⁶
We know that magnetic filed in wire at a distance r given as
By putting the values
r=0.032 m
r= 3.2 cm
Final answer:
The distance from a long straight wire at which the magnetic field equals the strength of Earth’s field, given a current of 8.7 A and Earth's field of 5.4 × 10−5 T, can be calculated using the formula for the magnetic field around a current-carrying wire. Substituting the given values, the answer is approximately 37.22 cm.
Explanation:
To solve this physics problem, we will use the formula for the magnetic field produced by a current carrying long, straight wire. The formula is: B = μI / (2πr), where 'B' is the magnetic field strength, 'μ' is the permeability of free space, 'I' is the current, and 'r' is the radial distance away from the wire.
In this case, Earth’s magnetic field, 'B', is given as 5.4 × 10−5 T, the current, 'I', is given as 8.7 A, and the permeability of free space, 'μ', is given as 1.25664 × 10−6 T · m/A. We need to find 'r', the distance away from the wire, and we want this answer in centimeters.
So, rearrange the formula to solve for 'r': r = μI / (2πB).
Substitute our known values into the equation: r = (1.25664 × 10−6 T · m/A × 8.7 A) / (2π × 5.4 × 10^-5 T). After calculating, we need to convert from meters to centimeters by multiplying by 100. The final answer is approximately 37.22 cm.
Learn more about Magnetic Field Calculation here:
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