Question

You take a running leap from a diving board at 1.5 m/s and hit the water 1.5 seconds later. How high was the diving board? Round to the nearest whole number.

a. 4 m
b. 8 m
c. 11 m
d. 16 m

Answer 1

Using the kinematic equation for free fall and accounting for the acceleration due to gravity, the height of the diving board is calculated to be 11 m when rounded to the nearest whole number. Thus, the answer to how high the diving board was is 11 m.

Step-by-step explanation:

To determine how high the diving board was, you can use the kinematic equation for uniformly accelerated motion, which is:

h = v_i × t + ½ × a × t^2

Here, h is the height, v_i is the initial velocity (1.5 m/s directed horizontally, so it doesn't affect vertical motion), t is the time in the air (1.5 seconds), and a is the acceleration due to gravity (-9.8 m/s^2 since it's directed downward). Note that we take the upwards direction as positive, hence the negative acceleration.

Since the initial velocity in the vertical direction is 0 m/s (the diver is not jumping upwards or downwards), the equation simplifies to:

h = ½ × (-9.8 m/s^2) × (1.5 s)^2 = -11.025 m.

The negative sign indicates the direction of displacement is downwards. Rounding to the nearest whole number, h = 11 m.

Therefore, the answer is: c. 11 m.