A ball is shot from the ground into the air. At a height of 0.1m, the velocity is observed to be v=7.7i + 6.4j in meters per second (i horizontal, j upward). What is the direction of the ball's velociry just before it hits the ground?
It has the same i component, but j reverses sign.
We need to be able to find an angle that it is at when it hits the ground
theta = aretan(jomponent/icomponent)
To find the direction of the ball's velocity just before it hits the ground, we need to determine the vertical component of the velocity. Since the velocity vector is given as v = 7.7i + 6.4j, where i is the horizontal component and j is the vertical component, we can see that the vertical component is 6.4j.
Since the ball is shot into the air, it will have an initial positive velocity in the vertical direction (upward). As it reaches its highest point and starts coming back down, the velocity vector will have a negative vertical component (downward).
Therefore, just before the ball hits the ground, the direction of the ball's velocity will be in the negative vertical direction or downward.