Final answer:
A football kicked to land 46m away after 4 seconds has a horizontal velocity of 11.5 m/s. The vertical velocity isn't provided in the options, but it can also be calculated using kinematic equations. The given options appear to have a mistake as none of them accurately describe the vertical velocity which must be more than the given value of 9.8 m/s.
Step-by-step explanation:
The question pertains to the calculation of horizontal and vertical velocities of a football kicked with a given horizontal distance and time of flight. To determine the correct horizontal and vertical velocities, we can use kinematic equations for projectile motion.
The horizontal velocity (vx) can be found using the formula:
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- Horizontal Distance = horizontal velocity * time
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- vx = Horizontal Distance / time
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- vx = 46m / 4s = 11.5 m/s
Assuming the vertical velocity (vy) equals the gravitational acceleration (g) at the peak of the path (since the velocity must be zero at the peak for the object to change direction), we calculate the half-time to reach the maximum height, which is half of the total time the football is in the air.
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- vy = g * (total time / 2)
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- vy = 9.8 m/s2 * (4s / 2)
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- vy = 9.8 m/s2 * 2s = 19.6 m/s
However, the correct answer is not included in the options given by the student. The actual initial vertical velocity is higher than 9.8 m/s since it takes the ball a certain amount of time to slow down to 0 m/s at its highest point due to gravity. The student's options suggest there might have been an oversight or misunderstanding in the question or the answer choices presented.