Erica is participating in a road race. the first part of the race is on a 5.2-mile-long straight road oriented at an angle of 25∘ north of east. the road then turns due north for another 5.0 mi to the finish line.
in miles, what is the straight-line distance from the starting point to the end of the race?

8.6 miles

Explanation:

We need to calculate the components of the total displacement along the east-west and north-south directions first.

In the first part, Erica moves 5.2 miles at 25∘ north of east. So the components of this displacement along the two directions are:

East:

North:

In the second part, Erica moves 5.0 miles north. So, the components of this displacement are:

East:

North:

So the components of the total displacement are

East:

North:

Therefore the magnitude of the displacement, which is the straight-line distance from the starting point to the end of the race, is

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s