A ball is thrown downward with an initial speed of 5 m/s from a height of 20 m.

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Question: A ball is thrown downward with an initial speed of 5 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)

Options:

Correct Answer: 3 s

Solution:

Using the equation of motion: h = ut + 0.5gt². 20 = 5t + 0.5 * 10 * t². Rearranging gives 5t + 5t² - 20 = 0. Solving the quadratic gives t = 2 s.

A ball is thrown downward with an initial speed of 5 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)

A ball is thrown downward with an initial speed of 5 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)

Step 1: Identify the known values. The initial speed (u) is 5 m/s, the height (h) is 20 m, and the acceleration due to gravity (g) is 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 = 5t + 0.5 * 10 * t².
Step 4: Simplify the equation: 20 = 5t + 5t².
Step 5: Rearrange the equation to set it to zero: 5t² + 5t - 20 = 0.
Step 6: Divide the entire equation by 5 to make it simpler: t² + t - 4 = 0.
Step 7: Use the quadratic formula to solve for t: t = (-b ± √(b² - 4ac)) / 2a, where a = 1, b = 1, and c = -4.
Step 8: Calculate the discriminant: b² - 4ac = 1² - 4*1*(-4) = 1 + 16 = 17.
Step 9: Substitute the values into the quadratic formula: t = (-1 ± √17) / 2.
Step 10: Calculate the two possible values for t. Since time cannot be negative, take the positive value: t ≈ 2 seconds.

Equations of Motion – The question tests the understanding of the equations of motion, particularly how to apply them to calculate the time of flight for an object under constant acceleration.
Quadratic Equations – The problem involves rearranging the motion equation into a quadratic form and solving it, which tests the ability to handle quadratic equations.
Kinematics – The scenario involves kinematic principles, specifically the motion of an object under the influence of gravity.