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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 h(t)=-16²+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?

User LeoE
by
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1 Answer

3 votes

Answer: 12 ft/s

Explanation:

We are told the following function models Spot's height at time
t:


h_(t)=-16t^(2)+20t (1)

And we are asked to find Spot's average rate of ascent, this means its velocity
V, which is calculated by:


V=\frac{h_{t=(1)/(2)}-h_(t=0)}{t_(f)-t_(o)} (2)

Where:


h_{t=(1)/(2) is the height of Spot at time
t=(1)/(2)s


h_{t=0 is the height of Spot at time
t=0 s


t_(f)=(1)/(2) s is the final time


t_(o)=0 s is the initial time

So, firstly we need to calculate
h_{t=(1)/(2) and
h_{t=0:


h_{t=(1)/(2)}=-16((1)/(2))^(2)+20((1)/(2)) (3)


h_{t=(1)/(2)}=6 ft (4)


h_(t=0)=0 ft (5)

Substituting these values in (2):


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

Finally:


V=12 ft/s This is Spot's average rate of ascent

User Stark Buttowski
by
8.1k points
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