A ball is thrown downwards with an initial velocity of 5 m/s from a height of 20
Practice Questions
Q1
A ball is thrown downwards with an initial velocity of 5 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
Questions & Step-by-Step Solutions
A ball is thrown downwards with an initial velocity of 5 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)
Correct Answer: 2 seconds
Step 1: Identify the variables in the problem. We have initial height (h) = 20 m, initial velocity (u) = 5 m/s, and acceleration due to gravity (g) = 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: 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, c = -4.
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, we 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.
Initial Velocity and Acceleration – It assesses the ability to incorporate initial velocity and gravitational acceleration into the motion equations.
Quadratic Equations – The problem requires solving a quadratic equation, which is a key skill in physics problems involving motion.
