You throw a ball straight down from an apartment balcony to the ground below. The ball has an initial velocity of 5.25 m/s, directed downward, and it hits the ground 1.94 s after it is released. Find the height of the balcony.
The vertical distance it falls in time t is:
Y = 5.25 t + (g/2) t^2
Plug in t = 1.94 s for your answer.
g = 9.8 m/s^2
To find the height of the balcony, we can use the equation of motion for free fall:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
In this scenario, the ball is thrown downward with an initial velocity of 5.25 m/s, and it takes 1.94 seconds to hit the ground. We can use this information to find the height of the balcony.
First, let's calculate the time it takes for the ball to reach its peak height (when its velocity becomes 0). In free fall motion, the time to reach the peak is half the total time of the motion.
t_peak = t_total / 2
= 1.94 s / 2
= 0.97 s
Now, we can use this time to calculate the height of the balcony:
h = (1/2) * g * t_peak^2
Plugging in the values:
h = (1/2) * 9.8 m/s^2 * (0.97 s)^2
= 4.9 m/s^2 * 0.9409 s^2
= 4.64541 m
Therefore, the height of the balcony is approximately 4.65 meters.