Answer :
The height of the diving board is 1.04 m
Explanation:
The motion of the swimmer is a projectile motion, so it consists of two independent motions:
- A uniform motion (constant velocity) along the horizontal direction
- An accelerated motion with constant acceleration (acceleration of gravity) in the vertical direction
We start by analyzing the horizontal motion. The velocity is constant and it is
[tex]v_x = 3.62 m/s[/tex]
And the horizontal distance covered is
[tex]d=1.68 m[/tex]
Therefore, we can find the total time of flight of the swimmer:
[tex]t=\frac{d}{v}=\frac{1.68}{3.62}=0.46 s[/tex]
Now we analyze the vertical motion: we can apply the following suvat equation
[tex]s=ut+\frac{1}{2}at^2[/tex]
where
s is the vertical displacement (the height of the diving board)
u = 0 is the initial vertical velocity
[tex]a=g=9.8 m/s^2[/tex] is the acceleration due to gravity
t = 0.46 s is the time of flight
Substituting, we find the height of the board:
[tex]s=0+\frac{1}{2}(9.8)(0.46)^2=1.04 m[/tex]
Learn more about projectile motion:
brainly.com/question/8751410
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