Answer:
The correct answer is 1.55m.
Explanation:
The time taken by the ball to reach the ground is denoted by t.
the acceleration due to gravity is denoted by a.
The initial speed is denoted by u.
The kinetic energy of the ball just after the ball hit the ground is denoted by [tex]KE_{a}[/tex] .
The speed of the ball just after the ball hit the ground is denoted by [tex]u_{a}[/tex].
The mass of the ball is denoted by m.
The height attained by the ball when the ball rebounds from the ground is denoted by h.
The final speed of the ball at a height h is denoted by [tex]v_{a}[/tex].
The velocity of the ball hitting the ground,
[tex]v=u-at[/tex]
[tex]v=0-9.8[/tex]×3.6
v = -35.28m/sec
The kinetic energy of the ball before the ball hit the ground,
[tex]KE_{b} =\frac{1}{2}mv^{2}[/tex]
[tex]KE_{b} =\frac{1}{2}[/tex]×0.025×[tex](-35.28)^{2}[/tex]
[tex]KE_{b}[/tex] = 15.55J
As given in the question,
[tex]KE_{a}=[/tex] 75% of [tex]KE_{b}[/tex]
[tex]\frac{1}{2}mu_{a} ^{2}=\frac{75}{100}[/tex]×15.55
[tex]\frac{1}{2}[/tex]×0.025×[tex]u_{a} ^{2}=\frac{75}{100}[/tex]×15.55
[tex]u_{a}[/tex] = 30.54m/sec
The final speed [tex]v_{a}[/tex] of the ball at a height of h is equal to zero.
By the equation,
[tex]v_{a}=u_{a}-2ah[/tex]
0 = 30.54 - 2 × 9.8 × h
h = 1.55m
So, the height attained by the ball when the ball rebounds from the ground is equal to 1.55m.