Question

A diver launches herself off a springboard. The height of the diver, in metres, above the pool

1 seconds after launch can be modelled by the following function:
h(1) = 51 - 101 + 10,10
How high is the springboard above the water?

Answer 1

The springboard's height above the water is found by evaluating the height function at the time of launch, which is 10 meters.

Step-by-step explanation:

The height of the springboard above the water can be found by evaluating the function h(t) = -5t2 + 10t + 10 at t=0, which represents the moment the diver launches off the springboard. The quadratic function represents the diver's height as a function of time, where -5t2 is the term for acceleration due to gravity (in negative because it's downwards), 10t is the initial upward velocity, and 10 is the initial height from the water. By substituting t for 0, we can find the height of the springboard:

h(0) = -5(0)2 + 10(0) + 10 = 10 meters

Therefore, the springboard is 10 meters above the water. When the diver is at the peak of her motion, this is the highest point she reaches from the springboard and just before she starts to fall back down towards the pool.