Question

A cliff diver jumps into the ocean from a cliff 60m high. the diver's height, in metres, after t seconds is given by h(t)=100-5.2t2 . determine the rate of change of the height of the diver after 5 seconds.

Answer 1

The rate of change of the diver's height after 5 seconds is found by calculating the derivative of the given height function, resulting in a value of -52 meters per second, indicating a downward velocity.

Step-by-step explanation:

The student is asking about the rate of change of the height of a cliff diver after 5 seconds, given a specific function for the diver's height over time. The function provided is h(t) = 100 - 5.2t2. To find the rate of change, we need to calculate the derivative of the height function with respect to time t.

First, we will find the derivative of h(t), which is h'(t) = -2 × 5.2t = -10.4t. Then we substitute t = 5 seconds into the derivative to find the rate of change at that instant. So h'(5) = -10.4 × 5 = -52. This means that after 5 seconds, the height of the diver is decreasing at a rate of 52 meters per second.