8.854 m/s is the speed of the box after it reaches bottom of the ramp.
Explanation:
From the figure we came to know that height of the block is 4 m.
We know that,
Total "initial energy of an object" = Total "final energy of an object
"
Total "initial energy of an object" is = "sum of potential energy" and "kinetic energy" of an object at its initial position.
[tex]\text { "g" acceleration due to gravity is } 9.8 \mathrm{m} / \mathrm{s}^{2}[/tex]
[tex]\text { Total initial energy }=\mathrm{m} \times \mathrm{g} \times \mathrm{h}_{\mathrm{i}}+\frac{1}{2} \mathrm{m} v_{i}^{2}[/tex]
Initial velocity is “0” as the object does not have starting speed
[tex]\text { Height of the block where the object is placed initially }\left(h_{i}\right) \text { is } 4 \mathrm{m} \text { . }[/tex]
[tex]\text { Total initial energy }=\mathrm{m} \times 9.8 \times 4+\frac{1}{2} \mathrm{m} 0^{2}[/tex]
Total initial energy = 39.2 × m
[tex]\text { Total final energy }=\mathrm{m} \times \mathrm{g} \times \mathrm{h}_{\mathrm{f}}+\frac{1}{2} m v_{f}^{2}[/tex]
[tex]\text { We need to find final velocity } v_f[/tex]
[tex]\text { Height of the block where the object is travelled to bottom (h_) is } 0 \mathrm{m} \text { . }[/tex]
[tex]\text { Total final energy }=\mathrm{m} \times 9.8 \times 0+\frac{1}{2} m v_{f}^{2}[/tex]
Now, Total initial energy of an object = Total final energy of an object
[tex]39.2 \times \mathrm{m}=0.5 \mathrm{m} v_{f}^{2}[/tex]
[tex]\frac{39.2}{0.5}=v_{f}^{2}[/tex]
[tex]v_{f}^{2}=78.4[/tex]
[tex]v_{f}=\sqrt{78.4}[/tex]
[tex]v_{f}=8.854 \mathrm{m} / \mathrm{s}[/tex]
Final speed is 8.854 m/s.
