A rocket car is traveling on a linear horizontal frictionless track when it suddenly runs out of fuel. The car has achieved a speed of 100 meters per second at the very moment the fuel is completely spent. The track then suddenly changes to a 30-degree incline from the horizontal.
(A) Calculate the maximum height above the horizontal track the car will rise just as it comes to a complete stop.
(B) Calculate the distance; measured along the inclined track, the car will travel before coming to a complete stop.
(C) Calculate the total travel time of the car on the inclined plane from the time it enters the track to the time it comes to a complete stop on the inclined track.
(D) Calculate the rate of deceleration of the car on the inclined track.
this is a question i had posted.following the instructions, I got the answers below, plz help check, thx!
(A)510m
(B)1020m
(C)10.2s
(D)-9.80m/s^2
anyone please help...
To help verify your answers, let's go through the calculations step by step:
(A) To calculate the maximum height above the horizontal track the car will rise before coming to a stop, we need to use the concept of conservation of energy: the car's kinetic energy at the beginning (when it runs out of fuel) will be converted entirely to gravitational potential energy at the maximum height.
First, find the mass of the car, which is not provided in the question. Without this information, we cannot calculate the height directly. Please check if the mass of the car is mentioned or if there is any other relevant information for this calculation.
(B) To calculate the distance the car will travel along the inclined track before coming to a complete stop, we can analyze the motion using the equations of motion and forces.
When the car runs out of fuel and the track becomes inclined, the gravitational force acting on the car will cause it to decelerate.
Using the equations of motion, we can calculate the distance traveled using the equation:
distance = (velocity^2) / (2 * acceleration)
where:
- velocity is the initial velocity of the car in the horizontal direction (100 m/s in this case)
- acceleration is the deceleration due to gravity on the inclined track, which can be calculated using the gravitational acceleration (g = 9.8 m/s^2) and the angle of inclination (30 degrees)
Let's calculate the distance traveled along the inclined track:
acceleration = g * sin(angle)
distance = (velocity^2) / (2 * acceleration)
= (100^2) / (2 * 9.8 * sin(30))
≈ 1020 m
(C) To calculate the total travel time of the car on the inclined plane, we can divide the distance traveled by the initial velocity in the horizontal direction:
time = distance / velocity
= 1020 / 100
= 10.2 s
(D) To calculate the rate of deceleration of the car on the inclined track, we can use the gravitational acceleration and the angle of inclination:
deceleration = g * sin(angle)
≈ -9.8 m/s^2 (since it acts in the opposite direction of motion)
Based on these calculations, it seems like your answers for (B), (C), and (D) are correct. However, please double-check if there is any missing information or any assumptions made in the question that might affect the answer to (A).