If a stone is thrown downward with a speed of 15m/s from a cliff that is 80m high, its height in meters, after t seconds is h(t) = 80-15t-4.9t^2. Determine the stone's average rate of change of the distance between 0s and 1s
1. -34,6m/s
2. 20.9m/s
3. 19.9m/s
4. 34.6m/s
since the interval is [0,1], the slope is
(f(1)-f(0))m/(1-0)s = (60.1 - 80)/1 = -19.9 m/s
To determine the stone's average rate of change of the distance between 0s and 1s, we can calculate the difference in height between these two time intervals and divide it by the difference in time.
Let's calculate the stone's height at t = 0s:
h(0) = 80 - 15(0) - 4.9(0)^2
h(0) = 80 - 0 - 0
h(0) = 80m
Now, let's calculate the stone's height at t = 1s:
h(1) = 80 - 15(1) - 4.9(1)^2
h(1) = 80 - 15 - 4.9
h(1) = 60.1m
The difference in height between 0s and 1s is:
Δh = h(1) - h(0)
Δh = 60.1 - 80
Δh = -19.9m
The difference in time between 0s and 1s is 1s.
Now, let's calculate the stone's average rate of change of the distance:
Average Rate of Change = Δh / Δt
Average Rate of Change = -19.9m / 1s
Average Rate of Change = -19.9m/s
Therefore, the stone's average rate of change of the distance between 0s and 1s is approximately -19.9m/s.
So, the correct answer is 3. -19.9m/s.
To determine the stone's average rate of change of the distance between 0s and 1s, we need to evaluate the function h(t) = 80 - 15t - 4.9t^2 at t = 0s and t = 1s, and then calculate the difference between the two values.
Let's start by evaluating h(t) at t = 0s:
h(0) = 80 - 15(0) - 4.9(0)^2
= 80 - 0 - 4.9(0)
= 80 - 0
= 80
Next, let's evaluate h(t) at t = 1s:
h(1) = 80 - 15(1) - 4.9(1)^2
= 80 - 15 - 4.9(1)
= 80 - 15 - 4.9
= 60.1
Now, let's calculate the average rate of change between these two values:
Average rate of change = (h(1) - h(0)) / (1 - 0)
= (60.1 - 80) / 1
= -19.9 / 1
= -19.9
Therefore, the stone's average rate of change of the distance between 0s and 1s is -19.9 m/s.