Solve Parachute Problem: Stone Drops from 58m Cliff

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In summary, the problem involves a parachute being dropped from a 58-m-high cliff with a constant velocity of 1.2m/s, followed by a stone being dropped 43s later. The question is whether the stone will catch up with the parachute before it reaches the ground. The solution involves using equations for finding final velocity and distance when initial velocity, acceleration, and time are known. The result is that the stone will catch up with the parachute before it reaches the ground, as the time needed for the parachute to reach the ground without interference from the stone is 48.3333s and the time needed for the stone to reach the ground without interference from the parachute is 3.440455594s, which is
  • #1
Cole07
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Stoned Parachute problem

problem:
A. A small parachute dropped from a 58-m-high cliff falls with a constant velocity of 1.2m/s. 43s after the parachute is dropped, a stone is dropped from the cliff. will the stone catch up with the parachute before it reaches the ground? yes or no?

B. how long would it take for the parachute to reach the ground if it didn't get hit by the stone?

C. How long would it take the stone to hit the ground if there were no interference from the parachute?

Solutions I have tried:


A. For this I need to know B & C and I know that c needs to be less than 5 seconds


B. For this I take the equation 1.2m/s = 58/t and i solve for t my answer is 48.3333


C. For this I know initial velocity is 0 I'm not sure about the final velocity acceleration is -9.8 and t is my unknown but I don't understand how to find it since I do not have my final velocity.

Can anyone please help me?
 
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  • #2
There is a well know equation for finding the final velocity if the initial velocity, acceleration, and distance moved are know. There is also a well known equation relating distance and time when the initial velocity and acceleration are known. Either of these will help you. Can you tell us what they are?
 
  • #3
Would this Work final velocity= square root of initial velocity squared+2a*d and the answer would be 33.71646482 then i would use final velocity= initial velocity+ a*t the answer would be 3.440455594s so since this is less than 5s the answer to A would be yes ? Is this correct?
 
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  • #4
Looks good
 

Related to Solve Parachute Problem: Stone Drops from 58m Cliff

1. How long does it take for the stone to reach the ground?

The time it takes for an object to fall from a certain height can be calculated using the equation t = √(2h/g), where t is the time, h is the height, and g is the acceleration due to gravity (9.8 m/s²). Plugging in the given height of 58m, we get t = √(2(58)/9.8) = 3.8 seconds. Therefore, it takes approximately 3.8 seconds for the stone to reach the ground.

2. What is the velocity of the stone when it reaches the ground?

The velocity of an object when it reaches the ground can be calculated using the equation v = gt, where v is the velocity, g is the acceleration due to gravity, and t is the time. Plugging in the value for t from the previous question (3.8 seconds) and g (9.8 m/s²), we get v = (9.8)(3.8) = 37.24 m/s. Therefore, the velocity of the stone when it reaches the ground is approximately 37.24 m/s.

3. What is the distance the stone travels before hitting the ground?

The distance an object travels during free fall can be calculated using the equation d = ½gt², where d is the distance, g is the acceleration due to gravity, and t is the time. Plugging in the values of g (9.8 m/s²) and t (3.8 seconds) from the first question, we get d = ½(9.8)(3.8)² = 69.88 meters. Therefore, the distance the stone travels before hitting the ground is approximately 69.88 meters.

4. How does air resistance affect the stone's descent?

Air resistance, also known as drag, can affect the speed and acceleration of an object falling through the air. In the case of this problem, the stone's descent will be affected by air resistance, causing it to reach a lower velocity and take longer to reach the ground compared to if it were falling in a vacuum. However, for the purpose of this problem, we can assume that air resistance is negligible.

5. Can this problem be solved using other methods besides equations?

Yes, this problem can also be solved using graphical methods such as position-time and velocity-time graphs. Additionally, advanced techniques such as numerical methods and computer simulations can also be used to solve this problem. However, the most common and efficient method is using the equations of motion mentioned in the previous answers.

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