Share
Distance Between Two Cars A car leaves an intersection traveling west. Its position 4 sec later is 19 ft from the intersection. At the same
Question
Distance Between Two Cars A car leaves an intersection traveling west. Its position 4 sec later is 19 ft from the intersection. At the same time, another car leaves the same intersection heading north so that its position 4 sec later is 26 ft from the intersection. If the speeds of the cars at that instant of time are 8 ft/sec and 12 ft/sec, respectively, find the rate at which the distance between the two cars is changing. (Round your answer to one decimal place.)
in progress
0
Physics
4 years
2021-08-16T02:31:08+00:00
2021-08-16T02:31:08+00:00 1 Answers
13 views
0
Answers ( )
Answer:
The answer to the question is;
The rate at which the distance between the two cars is changing is equal to 14.4 ft/sec.
Explanation:
We note that the distance traveled by each car after 4 seconds is
Car A = 19 ft in the west direction.
Car B = 26 ft in the north direction
The distance between the two cars is given by the length of the hypotenuse side of a right angled triangle with the north being the y coordinate and the west being the x coordinate.
Therefore, let the distance between the two cars be s
we have
s² = x² + y²
= (19 ft)² + (26 ft)² = 1037 ft²
s =
= 32.202 ft.
The rate of change of the distance from their location 4 seconds after they commenced their journeys is given by;
Since s² = x² + y² we have
→
which gives
We note that the speeds of the cars were given as
Car B moving north = 12 ft/sec, which is the y direction and
Car A moving west = 8 ft/sec which is the x direction.
Therefore