Obtain expressions in component form for the position vectors having the following polar coordinates: (a) 12.8 m, 150° (b) 3.30 cm, 60.0° (c) 22.0 in., 215°.

a) 12.8 m, 150° = (-11.09 i + 6.4 j) m

b)3.30 cm, 60.0° = (1.65 i + 2.86 j) cm

c)22.0 in., 215° = (-18.02 i + 9.30 j) in.

Explanation:

Consider  vector having magnitude X and inclined θ degree to positive horizontal axis, its horizontal component = X cosθ and vertical component =  X sinθ.

  So X = X cosθ i + X sinθ j

a)12.8 m, 150°

       = 12.8 cos 150 i + 12.8 sin 150 j = (-11.09 i + 6.4 j) m

b)3.30 cm, 60.0°

       = 3.30 cos 60 i + 3.30 sin 60 j = (1.65 i + 2.86 j) cm

c)22.0 in., 215°

       = 22.0 cos 215 i + 22.0 sin 215 j = (-18.02 i + 9.30 j) in.

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.