Respuesta :
Answer:
The height h, in terms of v, a, and g is h = 2·g·[tex](\frac{v}{a} )^2[/tex]
Explanation:
To find the solution, we list out the variables and their relationships
Height from which fire cracker is thrown = h
Speed with which fire cracker is thrown = v
Acceleration of wind in opposite direction of v = a
We have horizontal motion of the firecracker given by
S = v·t + 0.5·a·t² since a is in opposite direction to v, we have
S = v·t - 0.5·a·t² also since the firecracker comes to rest at the ground directly below the student we have displacement S = 0
Therefore S = v·t - 0.5·a·t² ⇒ 0 = v·t - 0.5·a·t², so that 0.5·a·t² = v·t or t = [tex]\frac{v}{0.5*a}[/tex]
= [tex]\frac{2v}{a}[/tex]
For the vertical motion, we have by Newton's law of motion
h = u·t + [tex]\frac{1}{2}[/tex]·g·t² however, u = 0
∴ h = [tex]\frac{1}{2}[/tex]·g·t² and substituting the value for t from the horizontal motion calculation solution, we have
h = [tex]\frac{1}{2}[/tex]·g·[tex](\frac{2v}{a})^2[/tex] = where g = 9.81 m/s², we have h = 19.62 [tex](\frac{v}{a} )^2[/tex] in terms of g we have h = 2·g·[tex](\frac{v}{a} )^2[/tex]
