Two golf balls are thrown with the same speed off the top of a large bridge at the same
time. Ball A is thrown straight downward, and Ball B is thrown horizontally off the
bridge. Which ball hits the ground first?
The 1st ball
h=v₀t₁+gt₁²/2
The 2nd ball
x=v₀t₂
h = gt₂²/2
t₁<t₂
To determine which ball hits the ground first, we need to consider two factors: the horizontal velocity and the vertical velocity of the balls.
Ball A is thrown straight downward, so it has an initial vertical velocity but no horizontal velocity. The initial vertical velocity of Ball A will cause it to accelerate due to gravity, increasing its downward speed.
Ball B is thrown horizontally off the bridge, so it has an initial horizontal velocity but no initial vertical velocity. Unlike Ball A, Ball B does not experience any vertical acceleration due to gravity, as gravity only acts vertically. Therefore, Ball B maintains a constant horizontal speed throughout its trajectory.
Now, since both balls are thrown at the same time, they both have the same amount of time to accelerate and fall. However, the horizontal motion of Ball B does not affect the time it takes to hit the ground, as it only acts on its horizontal position. The vertical motion, on the other hand, is affected by gravity for Ball A.
Since Ball A experiences vertical acceleration due to gravity while Ball B does not, Ball A will hit the ground first. This is because gravity accelerates any object in free fall at the same rate, regardless of its initial velocity.
In summary, both balls hit the ground simultaneously in terms of horizontal distance covered, but Ball A hits the ground first in terms of vertical distance covered.