Respuesta :
Answer:
Velocity is equal to [tex]27.3[/tex] feet per second and time is equal to [tex]1.4668[/tex] seconds
Explanation:
Given
The horizontal distance traveled by dirt bike before landing [tex]= 20[/tex] feet
Angle of flight [tex]= 60[/tex] degree
As we know that Horizontal distance (H) is equal to
[tex]= H_0 + V_0 * t\\[/tex]
Where [tex]H_0[/tex] is the initial horizontal distance
[tex]V_0[/tex] is the velocity with which the bike is travelling in horizontal direction
and [tex]t[/tex] is the time in seconds
Substituting the given values, we get -
[tex]H = H_0 + v*t\\20 = 0 + v * cos \theta * t\\20 = v * cos 60 * t\\t = \frac{20}{v * cos 60} \\t = \frac{40}{v}[/tex]
Now distance traveled in vertical direction is equal to
[tex]Y = Y_0 + v_0 * t + \frac{1}{2} a * t^2[/tex]
here acceleration will be equal to acceleration due to gravity which is equal to [tex]- 32.2 \frac{ft}{s^2}[/tex]. It is negative as its is acting in upward direction
Thus,
[tex]Y = 0 + v * sin 60 + \frac{1}{2} * (-32.2) * (\frac{40}{v} )^2\\0 = 0 + 0.866 v + \frac{-25760}{v^2} \\0.866 v = \frac{-25760}{v^2}\\v^3 = \frac{-25760}{0.866} \\v = 27.3[/tex]
Velocity is equal to [tex]27.3[/tex] feet per second and time is equal to [tex]1.4668[/tex] seconds
