A college regulation goal post for football has a horizontal bar at a height of
ID: 1590709 • Letter: A
Question
A college regulation goal post for football has a horizontal bar at a height of 3.048 m from the ground. A kicker attempts a field goal at a distance of 30 m. from the goal posts. The initial speed of the ball is 19 m/s making an angle of 40o above the horizontal. The plane of the trajectory is perpendicular to the plane of the goal posts. Neglect friction and air resistance.
a) The horizontal component of the initial speed of the ball is ______________m/s
b) The vertical component of the initial speed of the ball is ______________m/s
c) The time it takes for the ball to cross the plane of the goal posts is ______________ seconds.
d) The ball crosses the plane of the goal posts at a height of ______________m above the horizontal goal post.
e) The magnitude of speed of the football as it crosses the plane of the goal posts is ______________m/s.
Explanation / Answer
a) The horizontal component of the initial speed of the ball = 19 * cos 40
= 14.55 m/sec
b) The vertical component of the initial speed of the ball = 19 * sin 40
= 12.21 m/sec
c) The time it takes for the ball to cross the plane of the goal posts = 30/14.55
= 2.06 sec
d) Here, total height from ground = 12.21 * 2.06 - 0.5*9.8*2.06*2.06
= 4.36 m
=> ball crosses the plane of the goal posts at a height of above the horizontal goal post = 4.36 - 3.048
= 1.312 m
e) horizontal velocity = 14.55 m/sec
vertical velocity = 12.21 - 9.8*2.06
= -7.978 m/sec
=> magnitude of speed of the football as it crosses the plane of the goal posts = 16.593 m/sec
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.