An arrow is shot upward with speed 68 m/s, its height in meters t seconds later is given by y = 68t − 1.86t^2. Find average speed at [1,2],[1,1.5],[1,1.1],[1,1.01],[1,1.001].Estimate speed at t = 1

Answer 1

Assuming the question is asking for the average speed is over the x-intervals [1, 2], [1, 1.5], [1, 1.1], [1, 1.01], [1, 1.001], we find that average speed by taking [f(x₂) - f(x₁)]/(x₂ - x₁)

For [1, 2]: {[68(2) - 1.86(2)²] - [68(1) - 1.86(1)²]}/(2 - 1) = 62.42 m/s

For [1, 1.5]: {[68(1.5) - 1.86(1.5)²] - [68(1) - 1.86(1)²]}/(1.5 - 1) = 63.35 m/s

For [1, 1.1]: {[68(1.1) - 1.86(1.1)²] - [68(1) - 1.86(1)²]}/(1.1 - 1) = 64.094 m/s

For [1, 1.01]: {[68(1.01) - 1.86(1.01)²] - [68(1) - 1.86(1)²]}/(1.01 - 1) = 64.2614 m/s

For [1, 1.001]: {[68(1.001) - 1.86(1.001)²] - [68(1) - 1.86(1)²]}/(1.001 - 1) = 64.27814 m/s

To estimate the speed at 1, we can take even smaller increments like [1, 1.0001] which gives 64.2798 or [1, 1.00001] which gives 64.27998 or even [1, 1.000001] which gives 64.279998. It appears the speed at x = 1 is 64.28 m/s