punter kicks a fooball straight downfield from his own 35 yard line with initial

Question

punter kicks a fooball straight downfield from his own 35 yard line with initial velocity 80 feet per second at an angle of 35° above horizontal. The ball strikes his foot 2 feet above the ground. (a) What will the hang time of this punt be? (how long will the ball be in the air?) f%" (b) If there is no wind, will the punt land inside the 10 yard line without going over the goal line? (will the ball travel between 55 and 65 yards while in the air?) (c) If there is wind that creates acceleration of 8ft/s2 toward the sideline, how far off the original course will the ball land?

Explanation / Answer

a)

consider the motion in Y-direction or vertical direction

Voy = initial velocity = 80 Sin35 = 45.88 ft/s

a = acceleration = - g = - 32.2 ft/s2

Y = vertical displacement = 0

t = time of travel

using the equation

Y = Voy t + (0.5) a t2

0 = 45.88 t + (0.5) (- 32.2) t2

t = 2.85 sec

b)

consider the motion along the horizontal direction :

Vox = initial velocity = 80 Cos35 = 65.5 ft/s

X = horizontal displacement = ?

using the equation

X = Vox t = 65.5 x 2.85 = 186.675 ft = 62.225 yards

the ball will not land withing the 10 yard line

c)

consider the motion along the horizontal direction :

Vox = initial velocity = 80 Cos35 = 65.5 ft/s

X = horizontal displacement = ?

ax = acceleration = 8 ft/s2

using the equation

X = Vox t + (0.5) ax t2

X = (65.5) (2.85) + (0.5) (8) (2.85)2 = 219.2 ft = 73.1 yards

hence 73.1 - 62.225 = 10.875 yards more

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