If a high-diver performs a handstand dive (falls vertically) from a platform and enters the water with a velocity of 18.98 m/s, through which displacement will the diver have travelled? Express your answer from the platform to the ground and indicate the displacement in this direction
-18.36
Well, the high-diver must be quite talented to perform a handstand dive! Now, let's calculate the displacement.
Since the diver falls vertically, we can assume there is no horizontal displacement. Therefore, we only need to determine the vertical displacement.
To find the displacement, we need to use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (18.98 m/s)
u = initial velocity (0 m/s, as the diver starts from rest)
a = acceleration (9.8 m/s^2, due to gravity)
s = displacement
Rearranging the equation, we get:
s = (v^2 - u^2) / (2a)
Plugging in the values, we find:
s = (18.98^2 - 0^2) / (2 * 9.8)
s = 180.642 m
Therefore, the diver will travel approximately 180.642 meters downwards from the platform to the water.
Hope that dives straight into your curiosity!
To find the displacement of the diver, we need to calculate the vertical distance traveled by the diver while falling.
We can use the equation of motion to find the displacement (d) using initial velocity (u), final velocity (v), and acceleration due to gravity (g). In this case, the initial velocity is 0 m/s (since the diver is at rest before falling) and the final velocity is 18.98 m/s.
The equation we can use is:
v^2 = u^2 + 2ad
where v is the final velocity, u is the initial velocity, a is the acceleration, and d is the displacement.
We know the acceleration due to gravity is approximately 9.8 m/s^2. Plugging in the values we have:
(18.98 m/s)^2 = (0 m/s)^2 + 2 * 9.8 m/s^2 * d
d = (18.98 m/s)^2 / (2 * 9.8 m/s^2)
d ≈ 18.228 m
Therefore, the diver will have traveled approximately 18.228 meters in the vertical direction from the platform to the ground. The displacement is downward.
To find the displacement of the high-diver, we need to know the time it takes for the diver to reach the water. With the given information, we can use the equation of motion:
vf^2 = vi^2 + 2ad
Here:
- vf = final velocity of the diver when entering the water = 18.98 m/s
- vi = initial velocity of the diver (since the diver starts from rest) = 0 m/s
- a = acceleration of the diver (since the diver is falling vertically under gravity only) = -9.8 m/s^2 (negative because it is directed downwards)
- d = displacement of the diver
Now, let's solve the equation for d:
18.98^2 = 0^2 + 2(-9.8)d
361.0404 = -19.6d
Dividing both sides by -19.6:
d = 361.0404 / -19.6
d ≈ -18.44 meters
Since we are asked to indicate the displacement in the direction from the platform to the ground, the negative sign indicates that the displacement is in the downward direction. Therefore, the high-diver will have traveled approximately 18.44 meters downward.