A ball is thrown upward with an initial velocity of 20 m/s from a height of 5 meters. The height h of the ball at any time t can be modeled by the equation . Use the quadratic formula to find the time t when the ball hits the ground. The solution is t = _________.
Answer & Analysis
Analysis
Question Analysis
This question requires students to apply the quadratic formula to a real-world context, specifically a physics problem involving the motion of a ball.
Key Concept Explanation
The key concept here is the application of the quadratic formula to solve for the roots of a quadratic equation, which in this case represents the time when the ball hits the ground.
Step-by-step Solution
1. Identify the coefficients: , , .
2. Substitute into the quadratic formula: .
3. Simplify the expression under the square root: .
4. Further simplify:
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