Question

Far in space, where gravity is negligible, a 425 kg rocket traveling at 75 m/s in the +x-direction fires its engines. FIGURE EX11.10 shows the thrust force as a function of time. The mass lost by the rocket during these 30 s is negligible. At what time does the rocket reach its maximum speed? What is the maximum speed?

Accepted Answer

Step 1: Analyze the graph provided. The thrust force (F) is plotted as a function of time (t). The graph shows that the thrust force is constant at 800 N from t = 0 to t = 10 s, then decreases linearly to 0 N from t = 10 s to t = 25 s, and remains at 0 N from t = 25 s to t = 30 s. Step 2: Recall Newton's second law of motion, which states that the net force acting on an object is equal to the rate of change of its momentum. Since the mass of the rocket is constant, the acceleration (a) can be calculated using the formula: a=Fm, where F is the thrust force and m is the mass of the rocket. Step 3: To find the velocity of the rocket as a function of time, integrate the acceleration over time. The velocity change (Δv) can be calculated using the formula: Δv=adt. Break the integration into two intervals: (1) t = 0 to t = 10 s, where the force is constant, and (2) t = 10 s to t = 25 s, where the force decreases linearly. Step 4: For the interval t = 0 to t = 10 s, calculate the velocity change using the constant acceleration formula: Δv=at. For the interval t = 10 s to t = 25 s, use the linear force equation to express acceleration as a function of time and integrate to find the velocity change. Step 5: The rocket reaches its maximum speed when the thrust force becomes zero (at t = 25 s). Add the initial velocity (75 m/s) to the total velocity change calculated from both intervals to determine the maximum speed. The time at which the maximum speed occurs is t = 25 s.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Thrust Force

Acceleration

Kinematics