The earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. assuming the earth is a sphere with a radius of 6.38 × 106 m, determine the speed and centripetal acceleration of a person situated (a) at the equator and (b) at a latitude of 30.0° north of the equator.

Answer

given,

Radius of earth = 6.38 x 10⁶ m

angular velocity  =

                            =

                            =

a) at equator

velocity v   = R ω  = 6.38 x 10⁶ x 7.27 x 10⁻⁵

             v = 463.8 m/s

centripetal acceleration = R ω² = 6.38 x 10⁶ x (7.27 x 10⁻⁵)²

                                        = 0.0337 m/s²

b) at a latitude of 30.0° north of the equator

r = R cos θ  =  6.38 x 10⁶ cos 30⁰ =  3.19 x  10⁶ m

velocity v   = R ω  = 3.19 x  10⁶ x 7.27 x 10⁻⁵

            v = 231.9 m/s

centripetal acceleration = R ω² = 3.19 x  10⁶  x (7.27 x 10⁻⁵)²

                                        = 0.0168 m/s²

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles