A stone is tossed vertically into the air from ground level with an initial velocity of 15 m/s. Its height at time t is h(t)=15t-4.9t^2.
Compute the stone's average velocity over the time interval [0.5, 2.5].
It says the answer is .3, but I keep getting something not close to that...
To calculate the average velocity of the stone over the time interval [0.5, 2.5], we need to find the change in height and change in time during that interval.
Let's start by finding the height of the stone at the beginning and end of the interval:
h(0.5) = 15(0.5) - 4.9(0.5)^2 = 7.75
h(2.5) = 15(2.5) - 4.9(2.5)^2 = -30.625
Now we can find the change in height:
Change in h = h(2.5) - h(0.5)
Change in h = -30.625 - 7.75
Change in h = -38.375
Next, we find the change in time:
Change in t = 2.5 - 0.5
Change in t = 2
Now, we can calculate the average velocity:
Average velocity = Change in h / Change in t
Average velocity = -38.375 / 2
Average velocity = -19.1875
Since the answer provided is 0.3, it seems there may have been a mistake in your calculations or the given answer. Double-checking the calculations should help you find where the error lies.
To compute the average velocity over the time interval [0.5, 2.5], we need to find the height of the stone at both of these times and then calculate the change in height divided by the change in time.
Given the height function h(t) = 15t - 4.9t^2, let's find the height at t = 0.5:
h(0.5) = 15(0.5) - 4.9(0.5)^2
= 7.5 - 4.9(0.25)
= 7.5 - 4.9(0.0625)
= 7.5 - 0.30625
= 7.19375
Next, let's find the height at t = 2.5:
h(2.5) = 15(2.5) - 4.9(2.5)^2
= 37.5 - 4.9(6.25)
= 37.5 - 30.625
= 6.875
Now we can compute the average velocity by dividing the change in height by the change in time:
Average velocity = (change in height) / (change in time)
= (h(2.5) - h(0.5)) / (2.5 - 0.5)
= (6.875 - 7.19375) / 2
= (-0.31875) / 2
= -0.159375
It seems there was an error in the calculation. The correct average velocity over the time interval [0.5, 2.5] is approximately -0.159375 m/s, not 0.3 m/s.
avg velocity = (h(2.5) - h(.5) )/(2.5 - .5)
I get exactly .3