A ball is thrown vertically upward with a speed of 26.8 m/s from a height of 1.9 m. How long does the ball take to hit the ground after it reaches its highest point?
To find the time it takes for the ball to hit the ground after reaching its highest point, we can break down the motion of the ball into two parts: its upward motion and its downward motion.
First, let's find the time it takes for the ball to reach its highest point. We can use the equation that relates the initial velocity (v₀), final velocity (v), acceleration (a), and time (t) for an object in free fall:
v = v₀ + at
Since the ball is thrown vertically upward, the initial velocity (v₀) is 26.8 m/s (positive), the final velocity (v) at the highest point is 0 m/s, and the acceleration (a) is the acceleration due to gravity, which is approximately -9.8 m/s² (negative as it acts in the opposite direction to the initial velocity).
0 = 26.8 + (-9.8)t
Solving for t, we have:
-9.8t = -26.8
t = -26.8 / -9.8 ≈ 2.735 seconds
So, it takes approximately 2.735 seconds for the ball to reach its highest point.
Next, let's find the time it takes for the ball to hit the ground after reaching its highest point. We know that the total time for the ball's motion is twice the time it takes to reach the highest point. Therefore:
Total time = 2 * 2.735 ≈ 5.47 seconds
So, the ball takes approximately 5.47 seconds to hit the ground after reaching its highest point.