If a ball is thrown in the air with a velocity 44 ft/s, its height in feet t seconds later is given by y = 44t − 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

Question

If a ball is thrown in the air with a velocity 44 ft/s, its height in feet t seconds later is given by y = 44t − 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

anonymous · Answer

all of it

anonymous · Answer

Average velocity is :
$$V=\frac{ \Delta y }{ \Delta t }$$

anonymous · Answer

You can elaborate on the formula a little more:$$V=\frac{ \Delta y }{ \Delta t }=\frac{ 44(t+\Delta t)-16(t+ \Delta t)^2-44t+16t^2 }{ \Delta t}=44-32t-16 \Delta t$$ Before using this formula, make sure the ball is going up or down all the time in the interval. This can be checked finding the time of maximum height:44-32t=0--->t=44/32<2---> the ball has reached max height and is falling.