The following questions present a twist on the scenario above to test your understanding. suppose another stone is thrown horizontally from the same building. if it strikes the ground 56 m away, find the following values.
(a) time of flight 3.03 correct: your answer is correct. s
(b) initial speed 18.5 correct: your answer is correct. m/s
(c) speed and angle with respect to the horizontal of the velocity vector at impact 23.23 incorrect: your answer is incorrect. m/s your response differs from the correct answer by more than 10%. double check your calculations.

The first part of the text is missing, you can find on google:

"A ball is thrown horizontally from the roof of a building 45 m. If it strikes the ground 56 m away, find the following values."

Let's now solve the different parts.

(a) 3.03 s

The time of flight can be found by analyzing the vertical motion only. The vertical displacement at time t is given by

where

h = 45 m is the initial height

g = 9.8 m/s^2 is the acceleration of gravity

When y=0, the ball reaches the ground, so the time taken for this to happen can be found by substituting y=0 and solving for the time:

(b) 18.5 m/s

For this part, we need to analyze the horizontal motion only, which is a uniform motion at constant speed.

The horizontal position is given by

where

is the horizontal speed, which is constant

t is the time

At t = 3.03 s (time of flight), we know that the horizontal position is x = 56 m. By substituting these numbers and solving for vx, we find the horizontal speed:

The ball was thrown horizontally: this means that its initial vertical speed was zero, so 18.5 m/s was also its initial overall speed.

(c) 35.0 m/s at 58.1 degrees below the horizontal

At the impact, we know that the horizontal speed is still the same:

we need to find the vertical velocity. This can be done by using the equation

where

is the initial vertical velocity

g is the acceleration of gravity

t is the time

Substituting t = 3.03 s, we find the vertical velocity at the time of impact:

So the magnitude of the velocity at the impact (so, the speed at the impact) is

The angle instead can be found as:

so, 58.1 degrees below the horizontal.

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach