Answer:
(a) the height of the diving board is 22.896 m
(b) the horizontal distance traveled by the girl is 7.02 m
(c) if she had just drop off the board, her time to drop to the water would have been longer.
Explanation:
Given;
initial speed of the girl, u = 3.9 m/s
time to hit the water, t = 1.8 s
(a) the height of the diving board is calculated as;
h = ut + ¹/₂gt²
h = (3.9 x 1.8) + ¹/₂ x 9.8 x 1.8²
h = 7.02 + 15.876
h = 22.896 m
(b) the horizontal distance traveled by the girl is calculated as;
X = ut
X = 3.9 x 1.8
X = 7.02 m
(c) if she just drop off the board, then the initial speed will be zero;
h = ut + ¹/₂gt²
h = 0 + ¹/₂gt²
2h = gt²
[tex]t^2 = \frac{2h}{g} \\\\t = \sqrt{\frac{2h}{g} } \\\\t = \sqrt{\frac{2 \ \times\ 22.896 }{9.8} }\\\\t = 2.16 \ s[/tex]
Thus, if she had just dropped off the board, her time to drop to the water would have been longer.
