Question
I. Tom throws a rock horizontally off of a 40 ,0 m high cliff.How fast did he throw the rock if it hits the ground 45.0 m from the base of the cliff?
Solution
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KayaElite · Tutor for 8 years
Answer
Here's how to solve this projectile motion problem:
**1. Analyze the Vertical Motion:**
* **Known:**
* Vertical displacement (Δy) = -40.0 m (negative because it's downwards)
* Initial vertical velocity (Vy₀) = 0 m/s (since the rock is thrown horizontally)
* Acceleration due to gravity (g) = -9.8 m/s² (negative because it's downwards)
* **Unknown:** Time of flight (t)
* **Equation:** Δy = Vy₀*t + (1/2)*g*t²
* **Solve for t:**
-40.0 m = (0 m/s)*t + (1/2)*(-9.8 m/s²)*t²
-40.0 m = -4.9 m/s² * t²
t² = (-40.0 m) / (-4.9 m/s²)
t² = 8.16 s²
t = √(8.16 s²)
t ≈ 2.86 s
**2. Analyze the Horizontal Motion:**
* **Known:**
* Horizontal displacement (Δx) = 45.0 m
* Time of flight (t) = 2.86 s (calculated from vertical motion)
* **Unknown:** Initial horizontal velocity (Vx₀)
* **Equation:** Δx = Vx₀*t
* **Solve for Vx₀:**
45.0 m = Vx₀ * 2.86 s
Vx₀ = (45.0 m) / (2.86 s)
Vx₀ ≈ 15.7 m/s
**Answer:** Tom threw the rock horizontally with a speed of approximately 15.7 m/s.
**1. Analyze the Vertical Motion:**
* **Known:**
* Vertical displacement (Δy) = -40.0 m (negative because it's downwards)
* Initial vertical velocity (Vy₀) = 0 m/s (since the rock is thrown horizontally)
* Acceleration due to gravity (g) = -9.8 m/s² (negative because it's downwards)
* **Unknown:** Time of flight (t)
* **Equation:** Δy = Vy₀*t + (1/2)*g*t²
* **Solve for t:**
-40.0 m = (0 m/s)*t + (1/2)*(-9.8 m/s²)*t²
-40.0 m = -4.9 m/s² * t²
t² = (-40.0 m) / (-4.9 m/s²)
t² = 8.16 s²
t = √(8.16 s²)
t ≈ 2.86 s
**2. Analyze the Horizontal Motion:**
* **Known:**
* Horizontal displacement (Δx) = 45.0 m
* Time of flight (t) = 2.86 s (calculated from vertical motion)
* **Unknown:** Initial horizontal velocity (Vx₀)
* **Equation:** Δx = Vx₀*t
* **Solve for Vx₀:**
45.0 m = Vx₀ * 2.86 s
Vx₀ = (45.0 m) / (2.86 s)
Vx₀ ≈ 15.7 m/s
**Answer:** Tom threw the rock horizontally with a speed of approximately 15.7 m/s.
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