In the absence of air resistance, a projectile is launched from and returns to ground level. It follows a trajectory similar to that shown in Figure 3.10 and has a range of 15 m. Suppose the launch speed is doubled, and the projectile is fired at the same angle above the ground. What is the new range? ### Projectile Motion**Illustration of Projectile Motion**The diagram provided offers a comprehensive explanation of the trajectory in projectile motion. Here's a breakdown of the key elements illustrated:1. **Initial Velocity \((v_0)\):** - The trajectory begins with an initial velocity \(v_0\), which is directed at an angle \(\theta\) from the horizontal axis. - This initial velocity can be decomposed into two components: - \(v_{0x}\): The horizontal component of the initial velocity. - \(v_{0y}\): The vertical component of the initial velocity.2. **Velocity Components:** - The position and velocity of the projectile at any point in its path can be examined by separating the motion into horizontal and vertical components. - The horizontal axis is labeled as \( +x \). - The vertical axis is labeled as \( +y \).3. **Trajectory Path:** - The dashed line represents the parabolic path the projectile follows. - Gravity acts on the projectile, causing its vertical velocity component to change throughout its flight.4. **Maximum Height (\(H\)):** - The maximum height \(H\) is the highest vertical position reached by the projectile. - It occurs when the vertical component of the velocity (\(v_y\)) becomes zero.5. **Range (\(R\)):** - The range \(R\) is the horizontal distance traveled by the projectile from its launch point until it returns to the same vertical level (assumed to be the launch height).6. **Axis Orientation:** - The smaller inset graph reaffirms the orientation of the coordinate axes: - \(+y\) direction is upwards. - \(+x\) direction is rightwards.This illustration is crucial for understanding the principles of kinematics, specifically how initial velocity and gravity interact to influence the path of a projectile. By analyzing the components of motion separately, one can predict and calculate various parameters such as maximum height, time of flight, and range.

Name: In the absence of air resistance, a projectile is launched from and re
Uploaded: 2024-03-20T06:57:47.000Z
Channel: Bartleby
Description: In the absence of air resistance, a projectile is launched from and returns to ground level. It follows a trajectory similar to that shown in Figure 3.10 and has a range of 15 m. Suppose the launch speed is doubled, and the projectile is fired at the