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Rudik
3 months ago
6

The crossbar of a goal post on a professional American football field sits at a height of 3.05 meters (10 feet) above the field.

A football is placed on the ground at midfield so that it is 54.9 meters (60 yards) horizontally from the position of the crossbar. The ball is then kicked so that its initial velocity is 26.0 m/s (58.2 mph) at an angle of 35 degrees above the horizontal. Neglecting air friction, does the ball make it over the goal post and by how much?
A. Yes, the ball passes 2.83 meters above the crossbar
B. No, the ball passes 1.57 meters below the crossbar
C. No, the ball hits the ground before it reaches the crossbar
D No, the ball hits the crossbar
E. Yes, the ball passes 8.22 meters above the crossbar
Physics
1 answer:
Sav [3.1K]3 months ago
5 0

Answer:

A. Yes, the ball clears the crossbar by 2.83 meters

Explanation:

This situation pertains to projectile motion.

The horizontal velocity component of the ball is calculated as 26 cos 35 = 21.3 m/s

The vertical velocity component is 26 sin 35 = 14.9 m/s

The time taken to travel the horizontal distance to the goalpost, which is 54.9 m, is:

= distance / horizontal speed

= 54.9 / 21.3

= 2.577 seconds.

The vertical distance achieved during this time is:

h = ut - 1/2 gt², where u is the initial vertical velocity, and t = 2.577 seconds.

h = 14.9 x 2.577 - 0.5 x 9.8 x (2.577)²

= 38.39 - 32.54

= 5.85 m

Thus, the ball surpasses the crossbar by 5.85 - 3.05 = 2.8 m

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The full articulation of the query is

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