Question

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 49 fts. Its height in feet after t seconds is given by y = 49t-16t^2

Find the average velocity for the time period beginning when t = 3 and lasting
A. .01 s
B .005 s
C .002 s
D. .001 s

Answer 1

The question is about calculating the average velocity of a thrown ball over various time intervals using a quadratic equation to find the ball's position at specific times. By using the positions at the start and end of the interval and dividing by the interval duration, the average velocity is obtained.

The correct option is C.

Step-by-step explanation:

The average velocity V_avg over a time interval (Δt) is given by the formula:

V_avg = Δy / Δt

In this case, y = 49t - 16t^2, and you want to find the average velocity for the time period beginning at t = 3 and lasting for Δt.

Calculate the height at t = 3 seconds:

y_1 = 49(3) - 16(3)^2

Then calculate the height at t = 3 + Δ t:

y_2 = 49(3 + Δ t) - 16(3 + Δ t)^2

Subtract the two heights to find Δy:

Δ y = y_2 - y_1

Now, use the average velocity formula:

V_avg = {Δy} / {Δt}

The same steps apply to other time intervals such as 0.005 seconds and 0.002 seconds.

The correct option is C.

Answer 2

The average velocity for the time period beginning at t = 3 and lasting .001 s is 1 ft/s.

Step-by-step explanation:

The average velocity for the time period beginning when t = 3 and lasting .001 s can be calculated by finding the displacement during that time period. The displacement can be found by subtracting the height at the end of the time period from the height at the beginning of the time period. So, we need to find the height at t = 3 and t = 3.001.

Using the given equation, y = 49t - 16t^2, we can plug in t = 3 and t = 3.001 to find the heights at those times. Substituting t = 3 into the equation gives y = 49(3) - 16(3^2) = 147 - 144 = 3. Substituting t = 3.001 gives y = 49(3.001) - 16(3.001^2) = 147.049 - 144.048 = 3.001.

So, the displacement is 3.001 - 3 = 0.001 feet. The average velocity is equal to the displacement divided by the time period, which is 0.001/0.001 = 1 ft/s.