Will the Stone Catch Up with the Parachute Before Hitting the Ground?

[Cole07]

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.

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?

 

[Doc Al]

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

Good.

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.

You don't need to be given the final velocity--you have the distance.

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?

Absolutely correct!

But you could also do it with less work by using a different kinematic equation--one that relates distance, time, and acceleration.

 

[kyle8921]

I would approach this problem using the principles of kinematics, specifically the equations of motion. Let's break down each part of the problem and find the solutions using these equations.

A. First, we need to determine the time it takes for the parachute to reach the ground. Using the equation d = v0t + 1/2at^2, where d is the distance (58m), v0 is the initial velocity (0m/s), a is the acceleration (-9.8m/s^2), and t is the time, we can solve for t. Plugging in the values, we get t = 3.44 seconds. Since this is less than 43 seconds, the stone will not catch up to the parachute before it reaches the ground. The answer to A is no.

B. To find the time it takes for the parachute to reach the ground without interference from the stone, we can use the same equation as in A, but this time, the distance is unknown and we are solving for t. Plugging in the values, we get t = 3.85 seconds.

C. Similarly, to find the time it takes for the stone to hit the ground without interference from the parachute, we can use the same equation as in A, but this time, the initial velocity is unknown and we are solving for t. Plugging in the values, we get t = 2.92 seconds.

Therefore, the stone will hit the ground 2.92 seconds after it is dropped, and the parachute will reach the ground 3.85 seconds after it is dropped. Since 2.92 seconds is less than 5 seconds, the answer to A is still no.

In conclusion, the stone will not catch up with the parachute before it reaches the ground. This can be confirmed by using the equations of motion and solving for the time it takes for each object to reach the ground.