A person jumps off a diving board 4.3 above the water's surface into a deep pool. The person's downward motion stops 2.1 below the surface of the water.

What is the question?

To find the total distance the person jumps from the diving board to the bottom of the pool, we need to calculate the sum of the distance above the water's surface and the distance below the surface.

Distance above the water's surface = 4.3 m
Distance below the surface = 2.1 m

Total distance jumped = Distance above + Distance below
Total distance jumped = 4.3 m + 2.1 m

Calculating the sum, we get:

Total distance jumped = 6.4 meters.

To find the time it takes for the person to reach the water's surface after jumping off the diving board, we first need to calculate the distance the person falls.

Given:
Initial height above water's surface (H1) = 4.3 m
Final height below water's surface (H2) = 2.1 m

The distance the person falls (d) is the sum of H1 and H2:
d = H1 + |H2|

Since H2 is given with a negative sign, we need to take the absolute value to get the magnitude.

d = 4.3 m + |(-2.1 m)| = 4.3 m + 2.1 m = 6.4 m

Next, we can find the time taken (t) using the equation of motion that relates distance, acceleration due to gravity (g), and time:
d = (1/2) * g * t^2

Where g is the acceleration due to gravity, which is approximately 9.8 m/s^2.

Plugging in the values, we have:
6.4 m = (1/2) * 9.8 m/s^2 * t^2

Simplifying the equation:
t^2 = (2 * 6.4 m) / 9.8 m/s^2
t^2 = 1.31 s
t ≈ sqrt(1.31 s) = 1.14 s

Therefore, it takes approximately 1.14 seconds for the person to reach the water's surface after jumping off the diving board.