Math Problem Statement
Solution
The problem involves determining the height of a cliff from which a rock is thrown downward with an initial velocity of . The time it takes to hit the ground is , and we are given the kinematic equation:
Where:
- is the height of the cliff,
- is the initial velocity,
- is the acceleration due to gravity,
- is the time.
We will now calculate the height .
Let me compute that.The height of the cliff is approximately .
This matches option D in the given multiple-choice answers.
Would you like more details or have any further questions?
Here are 5 related questions:
- How would the height of the cliff change if the initial velocity were 0 m/s?
- What would happen if the rock were thrown upwards instead of downwards?
- How does air resistance affect the time taken for the rock to reach the ground?
- How does the equation of motion change if the rock were in a vacuum?
- What is the significance of the time squared term in the equation?
Tip: Remember that when dealing with projectile motion, initial velocity and time are key factors that determine the distance an object travels.
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Math Problem Analysis
Mathematical Concepts
Kinematics
Projectile Motion
Gravity
Formulas
Δd = v_i * t + 1/2 * g * t^2
Theorems
Kinematic equations of motion under constant acceleration
Suitable Grade Level
Grades 9-12
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