Final answer:
Using a kinematic equation, we can calculate the velocity of a diver when he strikes the water. The initial upward velocity and the height of the diving board are used to determine that the diver's final velocity is approximately -7.67 m/s, with the negative sign indicating the downward direction.
Step-by-step explanation:
To find the velocity at which the diver strikes the water, we can use the following kinematic equation that relates initial velocity, acceleration, displacement, and final velocity:
v² = v₀² + 2a(y - y₀)
Where:
- v is the final velocity
- v₀ is the initial velocity (1.8 m/s)
- a is the acceleration due to gravity (9.8 m/s²)
- y - y₀ is the displacement (since the diver is returning to the original elevation of the pool's surface, this is the negative of the height of the board, -3.0m)
Plugging in the values, we get:
v² = (1.8 m/s)² + 2(9.8 m/s²)(-3.0 m)
v = sqrt((1.8 m/s)² - 2(9.8 m/s²)(3.0 m))
v ≈ -7.67 m/s
The negative sign indicates the direction of the velocity is downward, while the magnitude gives us the speed at which he strikes the water.