a =-g = -9.81 m/s^2
v = Vi + a t = 0 - 9.81 t
h = Hi + Vi t + (1/2) a t^2 = Hi + 0 -4.9 t^2
h = 0 at water
Hi = 4.9 t^2
Hi = 4.9 (2.04)^2 = 20.4 meters
d = displacement from top = -20.4 m
v = Vi + a t = 0 - 9.81 t
h = Hi + Vi t + (1/2) a t^2 = Hi + 0 -4.9 t^2
h = 0 at water
Hi = 4.9 t^2
Hi = 4.9 (2.04)^2 = 20.4 meters
d = displacement from top = -20.4 m
If the diver falls vertically during a handstand dive, we can assume that their initial velocity is zero. We can use the equation of motion:
displacement = (initial velocity ร time) + (0.5 ร acceleration ร time^2)
Since the diver is falling downwards, we can take acceleration due to gravity (g) as -9.8 m/s^2.
So, putting the values in, we have:
displacement = (0 ร 2.04) + (0.5 ร (-9.8) ร (2.04)^2)
Now, let's calculate this without clowning around too much.
displacement = -20.03
Therefore, the displacement is -20.03 units (indicating downward direction) from the platform to the ground. And remember, gravity likes to pull us down, so it's a good idea not to keep too many things up in the air!
Displacement = Initial velocity ร time + (1/2) ร acceleration ร time^2
In this case, the diver starts from rest (initial velocity = 0) and falls vertically, so the acceleration will be equal to the acceleration due to gravity, which is approximately -9.8 m/s^2 (negative because it is downwards). Plugging in the given values:
Displacement = 0 ร 2.04 + (1/2) ร (-9.8) ร (2.04)^2
Simplifying the equation:
Displacement = -4.9 ร (2.04)^2
Calculating:
Displacement = -4.9 ร 4.1616
Displacement โ -20.3544
Therefore, the displacement of the diver is approximately -20.3544 units (downwards).
d = v0t + (1/2)gt^2
where:
d is the displacement (what we need to find)
v0 is the initial velocity (which is 0 since the diver starts from rest)
t is the time taken (given as 2.04 seconds)
g is the acceleration due to gravity (-9.8 m/s^2, as downward motion is negative)
Plugging in the given values, we have:
d = 0(2.04) + (1/2)(-9.8)(2.04)^2
Simplifying the equation:
d = 0 + (-4.9)(2.04)^2
d = -4.9(4.1616)
d = -20.36424
Therefore, the high-diver must have fallen a displacement of -20.36424 units (in the downward direction) from the platform to the ground.