Final answer:
The ball lands exactly at the bottom of the chute due to its horizontal motion being zero.
Step-by-step explanation:
In order to find how far from the bottom of the chute the ball lands, we need to first determine the time it takes for the ball to reach the ground. Given that the ball is thrown from a height of 98 m with an initial downward velocity of 4.9 m/s, we can use the equation:
h = v0t + 0.5at2
where h is the height, v0 is the initial velocity, a is the acceleration due to gravity, and t is the time. Since h = 0 (reaching the ground) and a = 9.8 m/s2, we can solve for t:
0 = 4.9t + 0.5(9.8)t2
t2 + 2t - 4.9 = 0
Using the quadratic formula, we find two solutions for t: t = -3.14 s and t = 1.14 s. We discard the negative solution as time cannot be negative in this context. Therefore, it takes approximately 1.14 seconds for the ball to reach the ground.
Now, to find how far from the bottom of the chute the ball lands, we can use the equation:
d = v0t
where d is the distance traveled horizontally and v0 is the initial velocity. Since the ball is thrown horizontally, the initial velocity in the horizontal direction is zero. Therefore, the ball lands exactly at the bottom of the chute.