A stone is thrown downward with an initial velocity of 5 m/s from a height of 45

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)

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)

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.

Equations of Motion – The question tests the understanding of the equations of motion, particularly how to apply them to calculate time of flight when an object is thrown with an initial velocity.
Quadratic Equations – The solution involves solving a quadratic equation, which is a key skill in physics problems involving motion.
Gravity and Acceleration – The problem incorporates the concept of gravitational acceleration and its effect on the motion of the stone.