d) Using Kinematics, derive an expression for the magnitude and direction angle of the projectiles velocity a time t after the object is fired. Check the physical units of your expression. e) Suppose that the projectile is fired with an initial speed of v, = 46.6 m/s and 0 = 42.2°, what is the magnitude and direction angle of the projectile's velocity t = 1.50 s after being fired?

College Physics
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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Need answer to part D and E

### Projectile Motion Problem

**Suppose a projectile is fired with initial speed \( v_0 \) and angle \( \theta \) above the horizontal.**

#### a) Understand and Plan

- **Task:** Draw a picture, establish a coordinate system for this problem, and label your diagram.
- **Action:** Make a table of known/given information and unknown/wanted information (this may involve reading the rest of the problem before starting).

#### b) Maximum Height Expression

- **Using Kinematics:** Derive a symbolic expression for the maximum height reached by the projectile.
- **Check:** Verify the physical units of your expression.

#### c) Total Time in Air

- **Using Kinematics:** Derive a symbolic expression for the total time the projectile is in the air.
- **Check:** Verify the physical units of your expression.

#### d) Velocity at Time \( t \)

- **Using Kinematics:** Derive an expression for the magnitude and direction angle of the projectile's velocity at time \( t \) after the object is fired.
- **Check:** Verify the physical units of your expression.

#### e) Given Initial Conditions

- **Problem Conditions:** Suppose that the projectile is fired with an initial speed of \( v_0 = 46.6 \, \text{m/s} \) and \( \theta = 42.2^\circ \).
- **Task:** Determine the magnitude and direction angle of the projectile’s velocity \( 1.50 \, \text{s} \) after being fired.
Transcribed Image Text:### Projectile Motion Problem **Suppose a projectile is fired with initial speed \( v_0 \) and angle \( \theta \) above the horizontal.** #### a) Understand and Plan - **Task:** Draw a picture, establish a coordinate system for this problem, and label your diagram. - **Action:** Make a table of known/given information and unknown/wanted information (this may involve reading the rest of the problem before starting). #### b) Maximum Height Expression - **Using Kinematics:** Derive a symbolic expression for the maximum height reached by the projectile. - **Check:** Verify the physical units of your expression. #### c) Total Time in Air - **Using Kinematics:** Derive a symbolic expression for the total time the projectile is in the air. - **Check:** Verify the physical units of your expression. #### d) Velocity at Time \( t \) - **Using Kinematics:** Derive an expression for the magnitude and direction angle of the projectile's velocity at time \( t \) after the object is fired. - **Check:** Verify the physical units of your expression. #### e) Given Initial Conditions - **Problem Conditions:** Suppose that the projectile is fired with an initial speed of \( v_0 = 46.6 \, \text{m/s} \) and \( \theta = 42.2^\circ \). - **Task:** Determine the magnitude and direction angle of the projectile’s velocity \( 1.50 \, \text{s} \) after being fired.
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