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Q.2

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 198

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Short Answer

A model rocket is on a cart that is rolling to the right at a speed of . The rocket engine, when it is fired, exerts an vertical thrust on the rocket. Your goal is to have the rocket pass through a small horizontal hoop that is above the ground. At what horizontal distance left of the hoop should you launch?

The horizontal distance between the hoop and the rocket should be .

See the step by step solution

Step by Step Solution

Step 1: Given Information

A model rocket is on a cart that is rolling to the right at a speed of ,

Step 2: Explanation

In this problem, the car moving horizontally with a speed, and while the car is moving, the rocket is launched vertically, which means the rocket will move with two components, in direction and in the direction where the rocket gains its component due to the movement of the car. The diagram below shows the situation. Where the rocket travels distances and where our target is to find that the rocket passes through the hoop.

First, let us calculate the time taken by the rocket to travel vertically . To find the time we should find the acceleration that the rocket gains due to the launch. The rocket is launched vertically due to its force against its weight. So, as the net force on the rocket will be given by

Step 3: Explanation

Now, we plug the values for and into equation (1) to get

The rocket starts from an initial position with an initial speed and time and reaches after travelling distance in time . We need to find the time by using the value of the calculated . The hoop is above the launch point, so the distance that the rocket travel is . From the kinematics equation, we can find the time by

Step 4: Explanation

Now, we plug the values for and into equation (2) to get

This is the time that taken for the rocket to pass from the hoop. so the rocket needs to travel horizontally in time

Step 5: Explanation

For the horizontal component, the rocket starts from an initial position is with an initial speed and reaches to the hoop after travelling distance in time . The rocket moves with constant speed, which means its acceleration equals zero . From the kinematics equation, we can find the distance by

Where is the horizontal distance between the hoop and the rocket to be launched. Now, we plug the values for and into equation (3) to get

Step 6: Final Answer

The horizontal distance between the hoop and the rocket should be .

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