Answer:
32 meters
Explanation:
Given:
x₀ = 0 m
y₀ = 1 m
y = 1 m
v₀ₓ = 18 cos 52° m/s
v₀ᵧ = 18 sin 52° m/s
aₓ = 0 m/s²
aᵧ = -9.8 m/s²
Find: x
First, find the time it takes for the ball to be caught.
y = y₀ + v₀ᵧ t + ½ aᵧt²
1 = 1 + 18 sin 52° t + ½ (-9.8) t²
0 = 14.2 t − 4.9 t²
0 = t (14.2 − 4.9 t)
t = 0 or 2.89
It takes 2.89 seconds to be caught. The horizontal distance traveled in that time is:
x = x₀ + v₀ₓ t + ½ aₓt²
x = 0 + (18 cos 52°) (2.89) + ½ (0) (2.89)²
x = 32.1
Rounded to two significant figures, the ball travels 32 meters.
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