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Example 3.7 Solution: Stone Thrown Horizontally from Cliff

  Horizontal Projectile Motion Problem Solved Step by Step

Dr.Sanjaykumar pawar

Diagram showing horizontal projectile motion of a stone thrown from a cliff with velocity, height, gravity, and curved trajectory labels.
A stone thrown horizontally from a 490 m cliff follows projectile motion under gravity.

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Example 3.7 Solution

Example 3.7 – Horizontal Projection Motion

Example 3.7 A hiker stands on the edge of a cliff 490 m above the ground and throws a stone horizontally with an initial speed of 15 m s-1. Neglecting air resistance, find the time taken by the stone to reach the ground, and the speed with which it hits the ground. (Take g = 9.8 m s-2 ).

A hiker stands on the edge of a cliff 490 m above the ground and throws a stone horizontally with an initial speed of 15 m s-1. Neglecting air resistance, find:

  • Time taken by the stone to reach the ground
  • Speed with which it hits the ground

Take g = 9.8 m s-2

Step 1: Write the Given Data

Height of cliff, h = 490 m
Initial horizontal velocity, ux = 15 m s-1
Initial vertical velocity, uy = 0
Acceleration due to gravity, g = 9.8 m s-2

Step 2: Find Time Taken to Reach the Ground

Use the equation of motion:

s = ut + ½gt²

Substitute the values:

490 = 0 × t + ½ × 9.8 × t²
490 = 4.9t²
t² = 490 / 4.9
t² = 100
t = √100
t = 10 s
Time taken to reach the ground = 10 s

Step 3: Find Vertical Velocity at Impact

Use the equation:

v = u + gt

Substitute the values:

vy = 0 + (9.8 × 10)
vy = 98 m s-1

Step 4: Horizontal Velocity Remains Constant

vx = 15 m s-1

Step 5: Find Resultant Speed at Impact

Use Pythagoras theorem:

v = √(vx² + vy²)

Substitute the values:

v = √(15² + 98²)
v = √(225 + 9604)
v = √9829
v ≈ 99.1 m s-1
Speed with which the stone hits the ground = 99.1 m s-1

Final Answers

1. Time taken = 10 s

2. Speed at impact = 99.1 m s-1
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