**Physics Problem: Projectile Motion**A daredevil drove his motorcycle up an incline at a 40-degree angle with the horizontal and drove off the end of the incline at 22 m/s, 12 meters above the ground. How fast was he (magnitude of total velocity) when he landed?---**Solution Explanation:**To solve this problem, we need to apply the principles of projectile motion. Here's a step-by-step guide on how to calculate the magnitude of the velocity when the daredevil lands.1. **Decompose the Initial Velocity:** - **Horizontal Component (Vx):** \[ Vx = V \cos(\theta) = 22 \, m/s \cdot \cos(40^{\circ}) \] \[ Vx \approx 16.85 \, m/s \] - **Vertical Component (Vy):** \[ Vy = V \sin(\theta) = 22 \, m/s \cdot \sin(40^{\circ}) \] \[ Vy \approx 14.14 \, m/s \]2. **Calculate the Time of Flight (t):** - Using the equation for vertical displacement under gravity: \[ y = Vy \cdot t + \frac{1}{2}gt^2 \] Here, \( y = -12 \, m \) (since the daredevil lands 12 meters below the takeoff point), and \( g = 9.8 \, m/s^2 \). Rearrange and solve the quadratic equation for \( t \): \[ -12 = 14.14 \, t - 4.9 \, t^2 \] Solving this quadratic equation gives \( t \approx 3.67 \, s \).3. **Calculate the Final Vertical Velocity (Vy_final) just before landing:** - Using the equation of motion: \[ Vy_{final} = Vy + gt \] \[ Vy_{final} = 14.14 - 9.8 \times 3.67 \] \[ Vy_{final} \approx -21.76 \, m/s \]4. **Calculate the Magnitude of the Total Velocity:** -

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A daredevil drove his motorcycle up an incline at 40 degree angle with the horizontal and drove off the end of the incline at 22 m/s, 12 m above the ground. How fast was him (magnitude of total velocity) when he landed?

A daredevil drove his motorcycle up an incline at 40 degree angle with the horizontal and drove off the end of the incline at 22 m/s, 12 m above the ground. How fast was him (magnitude of total velocity) when he landed?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Displacement, Velocity and Acceleration

In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.

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Topic Video

Question

**Physics Problem: Projectile Motion**

A daredevil drove his motorcycle up an incline at a 40-degree angle with the horizontal and drove off the end of the incline at 22 m/s, 12 meters above the ground. How fast was he (magnitude of total velocity) when he landed?

---

**Solution Explanation:**

To solve this problem, we need to apply the principles of projectile motion. Here's a step-by-step guide on how to calculate the magnitude of the velocity when the daredevil lands.

1. **Decompose the Initial Velocity:**
- **Horizontal Component (Vx):**
\[
Vx = V \cos(\theta) = 22 \, m/s \cdot \cos(40^{\circ})
\]
\[
Vx \approx 16.85 \, m/s
\]

- **Vertical Component (Vy):**
\[
Vy = V \sin(\theta) = 22 \, m/s \cdot \sin(40^{\circ})
\]
\[
Vy \approx 14.14 \, m/s
\]

2. **Calculate the Time of Flight (t):**
- Using the equation for vertical displacement under gravity:
\[
y = Vy \cdot t + \frac{1}{2}gt^2
\]
Here, \( y = -12 \, m \) (since the daredevil lands 12 meters below the takeoff point), and \( g = 9.8 \, m/s^2 \). Rearrange and solve the quadratic equation for \( t \):
\[
-12 = 14.14 \, t - 4.9 \, t^2
\]

Solving this quadratic equation gives \( t \approx 3.67 \, s \).

3. **Calculate the Final Vertical Velocity (Vy_final) just before landing:**
- Using the equation of motion:
\[
Vy_{final} = Vy + gt
\]
\[
Vy_{final} = 14.14 - 9.8 \times 3.67
\]
\[
Vy_{final} \approx -21.76 \, m/s
\]

4. **Calculate the Magnitude of the Total Velocity:**
-

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