Question

A student threw a ball horizontally out of a window 6.6 meters above the ground. It was caught by another student who was 18.3 meters away. What was the horizontal velocity of the ball?

a) 2 m/s
b) 3 m/s
c) 4 m/s
d) 5 m/s

Answer 1

The horizontal velocity of the ball can be calculated using the time it takes to fall the vertical distance due to gravity. However, the calculated value does not match any of the given options, suggesting there might be a mistake in the figures provided in the question or in the expected answers.

Step-by-step explanation:

Calculating Horizontal Velocity of a Projectile

To find the horizontal velocity of the ball, we need to use the information that the ball is thrown horizontally and caught by someone who is 18.3 meters away, while the vertical distance is 6.6 meters.

Since the ball is thrown horizontally, the initial vertical velocity is 0 m/s, and the only force acting on the ball in the vertical direction is gravity (9.81 m/s2). We can first calculate the time it takes for the ball to fall 6.6 meters using the formula for falling objects:

• y = 1/2 * g * t2

Solving for t (time), we get:

• 6.6 m = 1/2 * 9.81 m/s2 * t2
• t = sqrt((2 * 6.6 m) / 9.81 m/s2)
• t ≈ 1.16 seconds

Now that we know the time the ball was in the air, we can calculate the horizontal velocity:

• Horizontal distance = horizontal velocity * time
• 18.3 m = horizontal velocity * 1.16 s
• horizontal velocity ≈ 15.77586 m/s

However, since the options given in the question (a to d) do not contain this velocity, it suggests there might have been a mistake in the calculation or understanding of the problem. Since none of the provided answers are close to the calculated value, it is possible that the given distance or the height is incorrect, or the question expects a specific answer that hasn't been considered.