Arock (m= 2kg) is shot up vertically at the same time that a ball (m= 0.5kg) is projected horizontally. if both start from the same height: a. the rock and ball will reach the ground at the same time.
b. the rock will reach the ground first.
c. the ball will reach the ground first.
d. the rock and ball will collide in the air before reaching the ground.
can you explain why the answer is c?

The correct option is C. the ball will reach the ground first.

Explanation:

The ball will reach the ground first since the mass of each object does not affect the rate of fall, both are subject to the same gravitational acceleration 9.81 m / s2. The rock in its vertical movement invests a time that the ball is not released horizontally, so that time of vertical flight of the rock plus the extra height it will have will reach the ground after the rock. Regardless of the friction of the air, it will be different in both objects.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west