A stone is thrown downward with an initial velocity of 5 m/s from a height of 45 m. How long will it take to hit the ground? (2020)

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Q: A stone is thrown downward with an initial velocity of 5 m/s from a height of 45 m. How long will it take to hit the ground? (2020)

Solution: Using the equation of motion: h = ut + 0.5gt². Solving for t gives t ≈ 4 seconds.

Steps: 8

Step 1: Identify the variables in the problem. The initial height (h) is 45 meters, the initial velocity (u) is 5 m/s (downward), and the acceleration due to gravity (g) is approximately 9.8 m/s² (downward).
Step 2: Write down the equation of motion that relates height, initial velocity, time, and acceleration: h = ut + 0.5gt².
Step 3: Substitute the known values into the equation. Since the stone is thrown downward, we consider downward as positive: 45 = 5t + 0.5(9.8)t².
Step 4: Rearrange the equation to form a standard quadratic equation: 0 = 0.5(9.8)t² + 5t - 45.
Step 5: Simplify the equation: 0 = 4.9t² + 5t - 45.
Step 6: Use the quadratic formula t = (-b ± √(b² - 4ac)) / 2a, where a = 4.9, b = 5, and c = -45.
Step 7: Calculate the discriminant (b² - 4ac) to find the values of t.
Step 8: Solve for t using the quadratic formula to find the time it takes for the stone to hit the ground.