An arrow is fired with an initial velocity v0 at an angle θ0 above horizontal. Assume the arrow moves without air resistance. Use the Cartesian coordinate system provided, with the origin at the arrow's initial position. At some later time, t, the arrow makes an angle of θ with respect to the horizontal. Enter an expression for the time, t.

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An arrow is fired with an initial velocity v0 at an angle θ0 above horizontal. Assume the arrow moves without air resistance. Use the Cartesian coordinate system provided, with the origin at the arrow's initial position.

At some later time, t, the arrow makes an angle of θ with respect to the horizontal. Enter an expression for the time, t.

 

 

 

The image depicts the trajectory of a projectile, such as an arrow, in motion through the air. It illustrates the concept of projectile motion in physics.

**Description:**

- The projectile is shown at two points along its path: launch and during flight.
- It follows a curved, parabolic path, indicated by a dashed line, as it moves through the air.
- The launch angle, denoted by \( \theta_0 \), is the angle between the initial velocity vector \( v_0 \) and the horizontal axis \( x \).
- The arrow is initially launched from the ground, with its path extending upwards and curving downwards.
- As the projectile moves upwards, it reaches a peak, depicted near the top of the diagram, where the horizontal velocity component remains constant, but the vertical component becomes zero.
- The angle \( \theta \) at the descending point illustrates the angle of the projectile as it continues its path downward.

**Axes:**

- The \( x \)-axis represents the horizontal direction along the ground.
- The \( y \)-axis represents the vertical direction related to height or elevation from the ground.

This diagram serves as an educational representation of how projectiles behave when launched at an angle, taking into account both their vertical and horizontal components of motion, crucial for understanding fundamental principles of kinematics in physics.
Transcribed Image Text:The image depicts the trajectory of a projectile, such as an arrow, in motion through the air. It illustrates the concept of projectile motion in physics. **Description:** - The projectile is shown at two points along its path: launch and during flight. - It follows a curved, parabolic path, indicated by a dashed line, as it moves through the air. - The launch angle, denoted by \( \theta_0 \), is the angle between the initial velocity vector \( v_0 \) and the horizontal axis \( x \). - The arrow is initially launched from the ground, with its path extending upwards and curving downwards. - As the projectile moves upwards, it reaches a peak, depicted near the top of the diagram, where the horizontal velocity component remains constant, but the vertical component becomes zero. - The angle \( \theta \) at the descending point illustrates the angle of the projectile as it continues its path downward. **Axes:** - The \( x \)-axis represents the horizontal direction along the ground. - The \( y \)-axis represents the vertical direction related to height or elevation from the ground. This diagram serves as an educational representation of how projectiles behave when launched at an angle, taking into account both their vertical and horizontal components of motion, crucial for understanding fundamental principles of kinematics in physics.
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