# Projectile motion

1. Jan 8, 2008

### rocomath

You throw a ball with launch velocity of $$\overrightarrow {v_i}=(3m/s)\widehat{i}+(4m/s)\widehat{j}$$ toward a wall, where it hits at height $$h_1}$$ in time $$t_1$$ after the launch. Suppose that the launch velocity were, instead, $$\overrightarrow {v_i}=(5m/s)\widehat{i}+(4m/s)\widehat{j}$$.

Would the time taken by the ball to reach the wall be greater than, less than, or equal to $$t_1$$?

I thought that the horizontal component played no role in a projectile motion? Answer is less than, I would have chosen equal to. Should I compute the magnitude in order to convince myself other wise (course it would be greater for the 2nd).

Last edited: Jan 8, 2008
2. Jan 8, 2008

### blochwave

That's the ONLY component that matters here. Horizontal component is faster, gets there faster. When attempting to figure out how long it takes the ball to travel a horizontal distance, you're only interested in how fast it's going horizontally

Edit: So to make it even clearer, if the problem had the first case being 3 m/s horizontal and 45 sextillion m/s vertically, and the second case is 4 m/s horizontal but 3 nanometers/s vertical, answer is the same(EDIT and by the same I mean the same answer as the original question, which is the second one gets there faster)

Last edited: Jan 8, 2008