Answer:
The ball will drop 83 cm.
Explanation:
Hi there!
The equation of the position vector of the ball is the following:
r = (x0 + v0 · t, y0 + 1/2 · g · t²)
Where:
x0 = initial horizontal position.
v0 = initial horizontal velocity.
t = time
y0 = initial vertical positon.
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).
If we place the origin of the frame of reference at the throwing point, then:
x0 = 0 and y0 = 0. So, the equation of the position vector gets reduced to:
r = (v0 · t, 1/2 · g · t²)
Using the equation of the x-component of the position vector, let´s find the time at which the ball reaches the catcher:
x = v0 · t
x/v0 = t
17.0 m / 41.3 m/s = t
t = 0.412 s
Now, let´s calculate the y-component of the position vector to find how much the ball will drop in that time:
y = 1/2 · g · t²
y = -1/2 · 9.8 m/s² · (0.412 s)²
y = -0.832 m
The ball will drop 83 cm.
