The path of a baseball relative to the ground can be modelled by the function 𝑑(𝑡)=−𝑡2+8𝑡+1 where 𝑑(𝑡) represents the height of the ball in metres after 𝑡 seconds.Find the average rate of change of the ball between 1 and 3 seconds. Bold text start[4 marks]Bold text EndUsing the secant method, find the instantaneous rate of change at 2 seconds.

If a ball is thrown in the air with a velocity 50 ft/s, its height in feet t seconds later is given by y = 50t − 16t2.(a) Find the average velocity for the time period beginning when t = 2 and lasting(i)    0.5 second. ft/s(ii)    0.1 second. ft/s(iii)    0.05 second. ft/s(iv)    0.01 second. ft/s(b) Estimate the instantaneous velocity when t = 2. ft/s

Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above the ground. Find the velocity of the ball after 3 seconds.SolutionThe difficulty in finding the velocity after 3 seconds is that we are dealing with a single instant of time (t = 3), so no time interval is involved. However, we can approximate the desired quantity by computing the average velocity over the brief time interval of a tenth of a second from t = 3 to t = 3.1.average velocity  =  change in positiontime elapsed =  s(3.1) − s(3)0.1 =  4.9 2  − 4.9 2 0.1 =  m/s.The following table shows the results of similar calculations of the average velocity over successively smaller time periods.Timeinterval Averagevelocity (m/s)3 ≤ t ≤ 434.33 ≤ t ≤ 3.129.893 ≤ t ≤ 3.0529.6453 ≤ t ≤ 3.0129.4493 ≤ t ≤ 3.00129.4049It appears that as we shorten the time period, the average velocity is becoming closer to m/s (rounded to one decimal place). The instantaneous velocity when t = 3 is defined to be the limiting value of these average velocities over shorter and shorter time periods that start at t = 3. Thus the (instantaneous) velocity after 3 s is the following. (Round your answer to one decimal place.)v = m/s

A ball is thrown vertically upward froma height of 40 m and hits the groundwith a speed that is three times itsinitial speed. What is the time taken (insec) for the fall (Take 𝑔 = 10 𝑚/𝑠2) ?

When a baseball is hit, its height h (in meters) above the ground t seconds after being hit is given byht=−5t2+3​0t+1

New Question) 1 ptsGroup of answer choicesA linear trendline would be a better fit for representing the relationship between time and height.At 10 seconds the height of the ball is about 710 meters above the ground.The height of the ball at 20 seconds will be negative thus we can assume it will be underground.Higher balls cause an increase in the time in seconds.