chie left home and ran north for 20 minutes at 10 km/h and then turned north east for 35 minutes at 5 km/h. how far (km) was she away from home after the run?
d1 = 10km/h * (20/60)h = 3.33 km., N.
d2 = 5km/h * (35/60)h=2.92 km, NE.(45o)=
2.06 + 2.06i.
Disp.=2.06 + 2.06i + 3.33i=2.06 + 5.39i
= sqrt(2.06^2 + 5.39^2)
To find out how far Chie was away from home after the run, we can break down her movement into north and northeast components.
First, let's calculate the distance she covered running north for 20 minutes at 10 km/h. We can use the formula:
Distance = Speed × Time
Distance north = 10 km/h × (20 minutes ÷ 60 minutes/hour)
Distance north = 10 km/h × (1/3) hour
Distance north = 3.33 km
Next, let's calculate the distance she covered running northeast for 35 minutes at 5 km/h. Since she is running at a diagonal angle, we need to use trigonometry to calculate the distance. In a right-angled triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).
Given that Chie traveled for 35 minutes at 5 km/h, we can find the distance northeast using the formula:
Distance northeast = Speed × Time
Distance northeast = 5 km/h × (35 minutes ÷ 60 minutes/hour)
Distance northeast = 5 km/h × (7/12) hour
Distance northeast = 2.92 km
Now, we have the distances covered in each direction, north and northeast. To find the total distance from home, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Using the distances calculated earlier, we apply the Pythagorean theorem:
Total distance from home = √((Distance north)^2 + (Distance northeast)^2)
Total distance from home = √((3.33 km)^2 + (2.92 km)^2)
Total distance from home = √(11.0889 km^2 + 8.5264 km^2)
Total distance from home = √(19.6153 km^2)
Total distance from home = 4.43 km (rounded to two decimal places)
So, after the run, Chie was approximately 4.43 km away from home.