Question

Ian tosses a bone up in the air for his dog, Spot. The height, h, in feet, that Spot is above the ground at the time t seconds after she jumps for the bone can be represented by the function h(t)=-16t+20t. What is Spot's average rate of ascent, in feet per second, from the time she jumps into the air to the time she catches the bone at t=1/2 seconds

Answer 1

Hence the rate of ascent at t=1/2 is 12 ft/sec

Explanation:

Given:

Height function as h(t)=-16t^2+20t

To find:

Velocity at t=1/2. i.e. Average rate of ascent

Solution:

Average rate is given by

V=f(t)-f(a)/(t-a)

now here t=1/2 and a=0

Hence Equation becomes

V=f(1/2)-f(0)/(1/2-0)

So at t=1/2

f(1/2)=-16(1/2)^2+20(1/2)

=-4+10

=6 fts

Now ,t=0

f(0)=16(0)^2+20(0)

=0 ft

Hence V=f(1/2)-f(0)/(1/2-0)

V=(6-0)/(1/2-0)

V=6*2

V=12 ft/sec