Math Problem Statement
suppose you throw a ball straight up into the air with an initial speed of 50 meters per second. how high will the ball rise
Solution
To find the maximum height a ball reaches when thrown straight up, we can use the kinematic equation:
Where:
- = final velocity at maximum height (0 m/s, since the ball momentarily stops before descending)
- = initial velocity (50 m/s)
- = acceleration due to gravity (-9.8 m/s²; negative because gravity is acting in the opposite direction)
- = displacement or maximum height
Plugging in the values:
Simplifying:
Thus, the ball will rise to a maximum height of approximately 127.55 meters.
Would you like further details or have any questions?
Related Questions:
- How long will the ball take to reach its maximum height?
- What is the total time the ball will be in the air before hitting the ground?
- What will be the ball’s speed just before hitting the ground?
- How does the maximum height change if the initial velocity is doubled?
- How would the maximum height be affected if the gravitational acceleration is different?
Tip: When dealing with projectile motion, always identify which kinematic equation to use based on the known and unknown variables.
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Math Problem Analysis
Mathematical Concepts
Kinematics
Projectile Motion
Acceleration due to Gravity
Formulas
v^2 = u^2 + 2as
Theorems
Kinematic equations of motion
Suitable Grade Level
Grades 9-12
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