Calculating height in free falling problems

[akalei]

Homework Statement

A student stands at the edge of a vertical cliff and throws a stone vertically upwards. The stone leaves the student's hand with a speed of v=8.0m/s, the acceleration of free fall is 10m/s² and all distance measurements are taken from the point where the stone leaves the student's hand. Ignoring air resistance calculate the time taken by the stone to reach its maximum height.

The time between the stone's leaving Antionio's hand and hitting the sea is 3.0s. Determine the height of the cliff.

Homework Equations

unknown

The Attempt at a Solution

s= ut + 1/2at²
s= (8)(3) + 1/2(10)(3)²
s= 69

 

[PhanthomJay]

If you take positive as up, then negative is down. Which way does vo (u) act? Which way does the acceleration act? Which way is the displacement of the stone to the sea? Don't forget part a.

 

[akalei]

i think i understand what your saying but i don't understand how to use the information to solve the problem

 

[PhanthomJay]

For the equation you wrote for displacement, you have a signage error in one of the terms on the right side of the equation. Can you spot it??

 

[rwisz]

meters

I would like to clarify that the given information is not enough to accurately calculate the height of the cliff. The given time of 3.0 seconds only represents the total time for the stone to reach its maximum height and then fall back down to the sea. It does not provide the specific time at which the stone reaches its maximum height. In order to accurately calculate the height of the cliff, we would need to know the time at which the stone reaches its maximum height. This can be determined by using the equation v=u+at, where v is the final velocity (0 m/s at maximum height), u is the initial velocity (8.0 m/s in this case), a is the acceleration due to gravity (10 m/s2), and t is the time at which the stone reaches its maximum height. Once we have the time, we can use the equation s=ut+1/2at2 to calculate the height of the cliff. It is important to note that this calculation is only accurate if air resistance is truly ignored, as even a small amount of air resistance can affect the stone's trajectory and thus its maximum height.