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? (Assume g = 10 m/s²)

1 question

1 item

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? (Assume g = 10 m/s²)

Solution: Using the equation of motion: h = ut + 0.5gt². 45 = 5t + 0.5 * 10 * t². Solving the quadratic gives t = 3 s.

Steps: 10

Step 1: Identify the variables in the problem. The initial height (h) is 45 m, the initial velocity (u) is 5 m/s, and the acceleration due to gravity (g) is 10 m/s².
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: 45 = 5t + 0.5 * 10 * t².
Step 4: Simplify the equation: 45 = 5t + 5t² (since 0.5 * 10 = 5).
Step 5: Rearrange the equation to set it to zero: 5t² + 5t - 45 = 0.
Step 6: Divide the entire equation by 5 to make it simpler: t² + t - 9 = 0.
Step 7: Use the quadratic formula t = (-b ± √(b² - 4ac)) / 2a, where a = 1, b = 1, and c = -9.
Step 8: Calculate the discriminant: b² - 4ac = 1² - 4 * 1 * (-9) = 1 + 36 = 37.
Step 9: Substitute the values into the quadratic formula: t = (-1 ± √37) / 2.
Step 10: Calculate the two possible values for t. Since time cannot be negative, take the positive value: t ≈ 3 seconds.