Question

A horse and a squirrel participate in a race over a 1.20 km long course. The horse travels at a speed of 19.0 m/s and the squirrel can do 3.50 m/s. The horse runs for 0.960 km and then stops to tease the slow-moving squirrel, which eventually passes by. The horse waits for a while after the squirrel passes and then runs toward the finish line. Both animals cross the finish line at the exact same instant. Assume both animals, when moving, move steadily at their respective speeds.

(a)

How far (in m) is the squirrel from the finish line when the horse resumes the race?

m

(b)

For how long in time (in s) was the horse stationary?

s

Answer 1

Answer:

44.21053 m

279.69925 seconds

Explanation:

Time taken by the squirrel to reach the finish line

$\dfrac{1200}{3.5}=342.85714\ seconds$

Time taken by the horse to cover 0.96 km

$\dfrac{960}{19}=50.52631\ seconds$

Time taken by the horse to cover 1.2 km

$\dfrac{1200}{19}=63.15789\ seconds$

Let the distance that the squirrel is from the finish line when the horse resumes the race be x.

During this time the horse also reaches the finish line.

We deduce that

The time taken by the horse from one stop = Time taken by squirrel before x distance from finish line.

$3.5\times (63.15789-50.52631)=x\\\Rightarrow x=44.21053\ m$

The squirrel is 44.21053 m from the finish line when the horse resumes the race.

Duration is given by

$(342.85714-63.15789)=279.69925\ s$

The duration is 279.69925 seconds