A ball is thrown downward with an initial speed of 10 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)
Practice Questions
1 question
Q1
A ball is thrown downward with an initial speed of 10 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)
2 s
3 s
4 s
5 s
Using the equation of motion: h = ut + 0.5gt². 20 = 10t + 0.5 * 10 * t². Rearranging gives 5t² + 10t - 20 = 0. Solving this quadratic gives t = 2 s.
Questions & Step-by-step Solutions
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Q
Q: A ball is thrown downward with an initial speed of 10 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)
Solution: Using the equation of motion: h = ut + 0.5gt². 20 = 10t + 0.5 * 10 * t². Rearranging gives 5t² + 10t - 20 = 0. Solving this quadratic gives t = 2 s.
Steps: 11
Step 1: Identify the variables in the problem. We have initial speed (u) = 10 m/s, height (h) = 20 m, and acceleration due to gravity (g) = 10 m/s².
Step 2: Write down the equation of motion that relates height, initial speed, time, and acceleration: h = ut + 0.5gt².
Step 3: Substitute the known values into the equation: 20 = 10t + 0.5 * 10 * t².
Step 4: Simplify the equation: 20 = 10t + 5t².
Step 5: Rearrange the equation to set it to zero: 5t² + 10t - 20 = 0.
Step 6: Use the quadratic formula or factor the equation to find the value of t. The quadratic formula is t = (-b ± √(b² - 4ac)) / 2a.
Step 7: In our equation, a = 5, b = 10, and c = -20. Calculate the discriminant: b² - 4ac = 10² - 4 * 5 * (-20) = 100 + 400 = 500.
Step 8: Calculate t using the quadratic formula: t = (-10 ± √500) / (2 * 5).
Step 9: Simplify √500 to 10√5, then calculate t = (-10 ± 10√5) / 10 = -1 ± √5.
Step 10: Since time cannot be negative, take the positive solution: t = -1 + √5. Approximate √5 to about 2.236, so t ≈ 1.236 seconds.
Step 11: Round the answer to the nearest whole number if needed. In this case, we find that t ≈ 2 seconds.
