Math Problem Statement
Solution
The image you uploaded contains two projectile motion problems.
Problem 5:
- Situation: A stone is thrown from the top of a building that is 46.0 m high. It is thrown at an angle of 33.0° below the horizontal and strikes the ground 55.6 m away from the building.
- Questions:
- Time of flight: Calculate how long it takes for the stone to hit the ground.
- Initial speed: Determine the stone's initial velocity.
- Velocity before impact: Find the magnitude and direction of the stone’s velocity just before it hits the ground.
Problem 6:
- Situation: A baseball is hit with an initial speed of 30.0 m/s at an angle of 36.9° above the horizontal. Air resistance is ignored.
- Questions:
- Time at two heights: Find the two times at which the baseball is at a height of 10 m above the point where it was hit.
- Velocity components: Calculate the horizontal and vertical components of the baseball's velocity at each of these two times.
- Return velocity: Determine the magnitude and direction of the baseball’s velocity when it returns to the same height from which it was hit.
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Math Problem Analysis
Mathematical Concepts
Projectile Motion
Kinematics
Trigonometry
Formulas
s = ut + 1/2 at^2
v = u + at
Horizontal distance = u * cos(θ) * t
Vertical distance = u * sin(θ) * t - 1/2 * g * t^2
Magnitude of velocity = √(vx^2 + vy^2)
Angle of velocity = tan^(-1)(vy / vx)
Theorems
Equations of motion under constant acceleration
Trigonometric relationships in kinematics
Suitable Grade Level
Grades 11-12
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