Answer:
The rocket should be launched when the cart is 13.48m away from a point directly below the hoop.
Explanation:
Step 1: Data given
mass of the rocket = 600 grams
speed = 4.0 m/s
Step 2: Calculate weight
Fw = mg
with Fw = the weight (in Newton)
with m = the mass (in kg)
with g = the acceleration due to gravity (9.81 m/s²).
Fw = (0.600 kg)(9.81 m/s²) = 5.886 N
Step 3: Calculate force available to provide acceleration
The rocket engine, when it is fired, exerts a 8.0 AND vertical thrust on the rocket.
5.886 N of that force will be used to counter the rocket's weight, leaving 2.114 N of force available to provide acceleration.
Step 4: Calculate the rocket's upward acceleration:
Fnet = m*a
With Fnet = the net force (the force that remains after the rocket's weight is compensated)
with a = the rocket's acceleration (in m/s²)
2.114 N = (0.600 kg)*a
a = 3.52 m/s² = the rocket's upward acceleration
Step 5: Calculate how long it will take to rise 20 meters into the air.
Δy = v0*t + 1/2 at²
with v0 = 0m/s
Δy = 1/2 at²
20 m = 1/2(3.52)t²
20 m = (1.76 m/s²)t²
11.36 = t²
t = 3.37 s
This means the rocket will take 3.37 seconds to reach the hoop. It should be launched when the cart is 3.37 seconds away from being directly beneath the hoop.
Step 6: Calculate the distance
v = Δx / t
4.0 m/s = Δx / 3.37 s
Δx = 13.48 m
The rocket should be launched when the cart is 13.48m away from a point directly below the hoop.
