Respuesta :
Answer:
Impulse is 1.239 kg.m/s in upward direction
Explanation:
Taking upward motion as positive and downward motion as negative.
Downward motion:
Given:
Mass of ball (m) = 0.150 kg
Displacement of ball (S) = -1.25 m
Initial velocity (u) = 0 m/s
Acceleration is due to gravity (g) = -9.8 m/s²
Using equation of motion, we have:
[tex]v_d^2=u^2+2aS\\\\v=\pm\sqrt{u^2+2aS}\\\\v_d=\pm\sqrt{0+2\times -9.8\times -1.25}\\\\v_d=\pm\sqrt{24.5}=\pm4.95\ m/s[/tex]
Since, the motion is downward, final velocity must be negative. So,
[tex]v_d=-4.95\ m/s[/tex]
Upward motion:
Given:
Displacement of ball (S) = 0.665 m
Initial velocity ([tex]v_d[/tex]) = 4.95 m/s(Upward direction)
Acceleration is due to gravity (g) = -9.8 m/s²
Using equation of motion, we have:
[tex]v_{up}^2=v_d^2+2aS\\\\v_{up}=\pm\sqrt{v_d^2+2aS}\\\\v_{up}=\pm\sqrt{24.5+2\times -9.8\times 0.665}\\\\v_{up}=\pm\sqrt{10.966}=\pm3.31\ m/s[/tex]
Since, the motion is upward, final velocity must be positive. So,
[tex]v_{up}=3.31\ m/s[/tex]
Now, impulse is equal to change in momentum. So,
Impulse = Final momentum - Initial momentum
[tex]J=m(v_{up}-v_d)\\\\J=(0.150\ kg)(3.31-(-4.95))\ m/s\\\\J=0.150\ kg\times 8.26\ m/s\\\\J=1.239\ Ns[/tex]
Therefore, the impulse given to the ball by the floor is 1.239 kg.m/s in upward direction.
