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

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Question: 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)

Options:

Correct Answer: 4 s

Exam Year: 2020

Solution:

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

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)

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)

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.

Kinematics – The question tests the understanding of the equations of motion, specifically how to apply them to calculate the time of flight for an object in free fall with an initial velocity.
Initial Velocity – It assesses the ability to incorporate initial velocity into the motion equations when calculating the time to hit the ground.
Acceleration due to Gravity – The problem requires knowledge of gravitational acceleration (g = 9.81 m/s²) and its effect on the motion of the stone.