Answer:
a) Max height it will reach is 327.55 ft above the ground
b) It will reach max height after 5.1 seconds
c) It will be 300 feet off the ground at 12 seconds
d) It will be 305 ft above the ground
e) The rocket will be 247.55 ft above the ground after seven seconds
Explanation:
a) Using the equations of kinematics:
v² = v_i² + 2 g Δy
where
- v is the final velocity
- v_i is the initial velocity
- g is the acceleration due to gravity
- Δy is the rocket's displacement
Therefore,
0² = 50² + 2(- 9.8) Δy
(the negative sign shows that the positive direction is upwards. Gravity acts downwards)
Δy = -(50)² / 2(-9.8)
Δy = 127.55 ft
Thus, the maximum height that the rocket reaches will be
200 ft + 127.55 ft
= 327.55 ft above the ground
b) Using the equations of kinematics:
Δy = [(v + v_i) / 2 ] × t
t = Δy / [(v + v_i) / 2 ]
t = 127.55 / [(0 + 50) / 2]
t = 5.1 seconds
Therefore, the rocket will reach its maximum height after 5.1 seconds.
c) Using the equations of kinematics:
t₃₀₀ = Δy / [(v + v_i) / 2 ]
t₃₀₀ = 300 / [(0 + 50) / 2]
t₃₀₀ = 12 seconds
Therefore, the rocket will reach 300 feet after 12 seconds
d) Using the equations of kinematics:
Δy = [(v + v_i) / 2 ] × t
Δy = [(0 + 50) / 2] × 4.2
Δy = 105 ft
Therefore, the rocket will be
105 ft + 200 ft
= 305 ft above the ground after 4.2 seconds
e) Using the equations of kinematics:
Δy = [(v + v_i) / 2 ] × t
Δy = [(0 + 50) / 2] × 7
Δy = 175 ft
Therefore,
175 - 127.55 = 47.55 ft
Thus, the rocket will be
47.55 ft + 200 ft
= 247.55 ft above the ground after seven seconds