Respuesta :
Given data
*The given initial velocity is u = 5.5 m/s
*The given total time is T = 3.7 s
*The value of the acceleration due to gravity is g = -9.8 m/s^2
The formula for the time taken by the gourd to reach the highest point of the cliff is given by the equatin of motion as
[tex]v=u-gt[/tex]Here v = 0 m/s is the final velocity of the gourd at the highest point of the cliff
Substitute the known values in the above expression as
[tex]\begin{gathered} 0=5.5-(9.8)t \\ t=0.56\text{ s} \end{gathered}[/tex]The height of the cliff is calculated by the equation of motion as
[tex]\begin{gathered} s_1=ut-\frac{1}{2}gt^2 \\ =(5.5)(0.56)-\frac{1}{2}(9.8)(0.56)^2 \\ =1.54\text{ m} \end{gathered}[/tex]Hence, the height of the cliff is s_1 = 1.54 m
The time taken by the gourd to reach the peak height is calculated as
[tex]\begin{gathered} t_1=T-t \\ =3.7-0.56 \\ =3.14\text{ s} \end{gathered}[/tex]The formula for the peak height is given by the equation of motion as
[tex]s_2=\frac{1}{2}gt^2_1[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} s_2=\frac{1}{2}(9.8)(3.14)^2 \\ =48.3\text{ m} \end{gathered}[/tex]Hence, the peak height is s_2 = 48.3 m
The formula for the velocity of the gourd strikes into the ground below is given as
[tex]v=\sqrt[]{2gs_2}[/tex]Substitute the known values in the above expression asv=
[tex]\begin{gathered} v=\sqrt[]{2\times9.8\times48.3} \\ =30.76\text{ m/s} \end{gathered}[/tex]Hence, the velocity of the gourd smash into the ground is v = 30.76 m/s
