Answer:
10.1 m
Explanation:
The rocket engine exerts a upwards vertical force on the rocket, and gravity exerts a downwards vertical force. From Newton's second law of motion, the net force on an object is equal to its mass times its acceleration. Once the vertical acceleration is found, we can use kinematics to find the time it takes the rocket to reach the hoop, and then find the horizontal distance traveled in that time.
Applying Newton's second law:
∑F = ma
F − mg = ma
8.0 N − (0.600 kg) (9.8 m/s²) = (0.600 kg) a
a = 3.53 m/s²
Given in the vertical direction:
s = 20 m
u = 0 m/s
a = 3.53 m/s²
Find: t
s = ut + ½ at²
20 = (0) t + ½ (3.53) t²
t = 3.36 s
Given in the horizontal direction:
u = 3.0 m/s
a = 0 m/s²
t = 3.36 s
Find: s
s = ut + ½ at²
s = (3.0) (3.36) + ½ (0) (3.36)²
s = 10.1 m
