A person on an apartment balcony holds a ball over the balcony and throws it directly upwards with an initial velocity of 30 m/s [up]. The ball was thrown from 15 m above the ground. How long will it take for the ball to hit the ground?
Solve this equation for t:
(height above ground) =
15 + 30t - (g/2) t^2 = 0
where g is the accleration of gravity
To find the time it takes for the ball to hit the ground, we need to consider the motion of the ball in two parts: the upward motion when it is thrown and the downward motion when it comes back down.
First, let's calculate the time it takes for the ball to reach its highest point during the upward motion. We can use the kinematic equation:
v = u + at
Where:
v is the final velocity (0 m/s at the highest point),
u is the initial velocity (30 m/s),
a is the acceleration (due to gravity, approximately -9.8 m/s^2),
and t is the time.
Rearranging the equation to solve for time (t), we get:
t = (v - u) / a
Plugging in the values:
t = (0 - 30) / -9.8
t = 3.06 seconds (rounded to two decimal places)
So it takes 3.06 seconds for the ball to reach its highest point during the upward motion.
Next, we need to calculate the time it takes for the ball to fall back down from its highest point to the ground. The magnitude of the time will be the same as the time taken during the upward motion.
Therefore, the total time it takes for the ball to hit the ground is twice the time calculated above:
Total time = 2 * 3.06 seconds
Total time = 6.12 seconds (rounded to two decimal places)
Thus, it will take approximately 6.12 seconds for the ball to hit the ground.