Answer:
883.7 m
Explanation:
The baseball is in free fall. Neglecting air resistance, projectiles can be modeled using constant acceleration in both the horizontal and vertical direction. The kinematic equation that applies is:
s = ut + ½ at²
where s is the displacement, u is the initial velocity, a is the acceleration, and t is time.
First, find the time it takes the ball to land. In the y direction, the displacement is zero, since the ball returns to its original level, and the acceleration is the acceleration due to gravity.
s = 0 m
u = 100 sin 30 = 50 m/s
a = -9.8 m/s²
Find: t
s = ut + ½ at²
0 = 50t + ½ (-9.8) t²
0 = 50t − 4.9 t²
0 = 50 − 4.9 t
t = 10.2
Next, in the x direction, the acceleration is zero, since there's no forces acting on the ball in the horizontal direction.
u = 100 cos 30 = 86.6 m/s
a = 0 m/s²
t = 10.2 s
Find: s
s = ut + ½ at²
s = (86.6) (10.2) + ½ (0) (10.2)²
s = 883.7
Therefore, the ball will land approximately 884 meters away from the throwing point.
