Final answer:
The initial velocity of the rocket is -1350 m/s. The question involves applying principles of projectile motion and kinematics to a rocket launched at an angle with initial acceleration, addressing both the powered and free-fall phases of its flight.
Step-by-step explanation:
In this question, we have a rocket launched at an angle of 70° above the horizontal from rest. It moves for 30s with an acceleration of 45m/s². After 30 seconds, the engines fail and the rocket moves as a free body. To find the initial velocity of the rocket, we can use the formula:
v = u + at
where v is the final velocity (0 m/s), u is the initial velocity (unknown), a is the acceleration (45 m/s²), and t is the time (30 s). Rearranging the formula, we get:
u = v - at
Substituting the given values, we have:
u = 0 - (45 m/s²)(30 s)
Simplifying, we find:
u = -1350 m/s
The question involves applying principles of projectile motion and kinematics to a rocket launched at an angle with initial acceleration, addressing both the powered and free-fall phases of its flight.
The student's question is concerning projectile motion and the physics of a rocket moving under the influence of gravity and acceleration. In this scenario, the rocket is launched at a significant angle above the horizontal and follows a curved trajectory due to the acceleration of 45m/s2 for 30 seconds before moving freely as a projectile. The student seeks to understand the characteristics of the rocket's motion during and after powered acceleration.
To solve similar problems, one must apply the equations of motion to determine the rocket's final velocity after the period of acceleration, and then use projectile motion principles to calculate its trajectory once the engines fail. This involves breaking down the motion into horizontal and vertical components, taking into account gravity's constant acceleration of approximately 9.81m/s2 downward, and ignoring air resistance.