Respuesta :
Given,
The mass of the object, m=7.20 kg
The angle of projection, θ=55.0°
The time of flight, t=3.40 s
The time of flight of a projectile is given by,
[tex]t=\frac{2u\times sin\theta}{g}[/tex]Where u is the initial velocity and g is the acceleration due to gravity.
On substituting the known values,
[tex]\begin{gathered} 3.40=\frac{2\times u\times sin55^{\circ}}{9.8} \\ \Rightarrow u=\frac{3.40\times9.8}{2\times sin55^{\circ}} \\ =20.34\text{ m/s} \end{gathered}[/tex]Thus the y-component of the initial momentum is,
[tex]p_{iy}=mu\sin \theta[/tex]On substituting the known values,
[tex]\begin{gathered} p_{iy}=7.20\times20.34\times\sin 55^{\circ} \\ =119.96\text{ kg}\cdot\frac{m}{s} \end{gathered}[/tex]The y-component of the final velocity can be calculated using one of the equations of the motion,
[tex]v_y=u_{}\sin \theta-gt[/tex]On substituting the known values,
[tex]\begin{gathered} v_y=20.34\times\sin 55^{\circ}-9.8\times3.40 \\ =-16.66\text{ m/s} \end{gathered}[/tex]Thus the y-component of the final momentum is
[tex]p_{fy}=mv_y_{}[/tex]On substituting the known values,
[tex]\begin{gathered} p_{fy}=7.20\times-16.66 \\ =-119.95\text{ kg}\cdot\frac{m}{s} \end{gathered}[/tex]The y-component of the change in the momentum is given by,
[tex]\Delta p_y=p_{fy}-p_{iy}[/tex]On substituting the known values,
[tex]\begin{gathered} \Delta p_y=-119.95-119.96 \\ =-239.91\text{ kg}\cdot\frac{m}{s} \end{gathered}[/tex]Thus the y-component of the object's change in momentum is -239.91 kg·m/s
The negative sign indicates that the change is directed downwards.
