Answer:
The velocity is 7.0m/s
Explanation:
Given
[tex]mass (m) = 1kg[/tex]
[tex]height (h) = 2.5m[/tex]
[tex]g = 9.8m/s^2[/tex]
Required
The bottom of the plane velocity
To do this, we apply the work-energy theorem which states that the energy at the highest point and at the lowest point are equal.
At the highest point
[tex]v = 0[/tex]
[tex]E = \frac{1}{2}mv^2 + mgh[/tex]
[tex]E = \frac{1}{2}*1*0^2+ 1 * 9.8 * 2.5[/tex]
[tex]E = 0 + 24.5[/tex]
[tex]E = 24.5[/tex]
At the lowest point
[tex]h = 0[/tex]
[tex]E = \frac{1}{2}mv^2 + mgh[/tex]
[tex]E = \frac{1}{2} * 1 * v^2 + mg(0)[/tex]
[tex]E = \frac{1}{2} * 1 * v^2 + 0[/tex]
[tex]E = \frac{v^2}{2}[/tex]
Equate both values of energy
[tex]24.5 = \frac{v^2}{2}[/tex]
[tex]v^2 = 2 * 24.5[/tex]
[tex]v^2 = 49[/tex]
Take square roots of both sides
[tex]v = 7[/tex]
The velocity is 7.0m/s
