You throw a ball straight into the air from a height of 4 feet and with a speed of 8.22 m/s. The moment the ball leaves your hand you start running away at a speed of 3.36 m/s. How far are you from the ball, the moment it hits the ground?
See previous post: Mon,2-3-14,5:42 PM.
1.5s
To determine how far you are from the ball when it hits the ground, you need to consider the time it takes for the ball to fall and the distance you traveled while running.
First, let's calculate the time it takes for the ball to fall back to the ground. We can use the formula for freefall motion:
h = (1/2) * g * t^2,
where h is the initial height (4 feet) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Converting the initial height to meters:
h = 4 feet = 4 * 0.3048 = 1.2192 meters.
Plugging in the values:
1.2192 = (1/2) * 9.8 * t^2.
Simplifying the equation:
9.8 * t^2 = 2.4384,
t^2 = 2.4384 / 9.8,
t^2 ≈ 0.2489,
t ≈ √0.2489,
t ≈ 0.4989 seconds.
Now that we know the time it takes for the ball to fall, we can calculate the distance you traveled while running:
Distance = Speed * Time,
Distance = 3.36 m/s * 0.4989 s,
Distance ≈ 1.674 meters.
Therefore, you are approximately 1.674 meters away from the ball the moment it hits the ground.