A ball rolls off a 5 meter high deck at 5 m/s. How far will the ball move in the x-direction before it hits the ground?dx ≈ 4.1 mdx ≈ 9.1 m dx ≈ 3.1 mdx ≈ 5.1 m
Question
A ball rolls off a 5 meter high deck at 5 m/s. How far will the ball move in the x-direction before it hits the ground?dx ≈ 4.1 mdx ≈ 9.1 m dx ≈ 3.1 mdx ≈ 5.1 m
Solution
To solve this problem, we need to find out how long the ball is in the air (time of flight) and then use that time to find out how far the ball will move in the x-direction.
Step 1: Find the time of flight We can use the equation of motion to find the time it takes for the ball to hit the ground. The equation is:
h = 0.5 * g * t^2
where: h = height = 5 m g = acceleration due to gravity = 9.8 m/s^2 t = time
Rearranging the equation to solve for t gives:
t = sqrt((2h)/g) = sqrt((25)/9.8) = 1.01 s
Step 2: Find the distance in the x-direction The distance the ball will move in the x-direction (dx) can be found using the equation:
dx = v * t
where: v = velocity = 5 m/s t = time = 1.01 s
So, dx = 5 * 1.01 = 5.05 m
Therefore, the ball will move approximately 5.1 m in the x-direction before it hits the ground. So, the answer is dx ≈ 5.1 m.
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