During a football game, the kicker punts the football from the 35 yard line. The maximum height of the football is 15 yards. The football travels 40 yards through the air before it hits the ground.

Question

During a football game, the kicker punts the football from the 35 yard line. The maximum height of the football is 15 yards.

The football travels 40 yards through the air before it hits the ground.

Answer 1

It's probably above the 45 yard line of the opposing team, when it reaches maximum height, going half the distance until it hits the ground. It hits the ground in 40 yards. Half is 20 yards. 35+20 = 55. At the 50 yard line you're into the opposing teams' side. 55 from home team's end zone is 45 from the opposing team's end zone. The ball is above the 45 yard line

UNLESS the problem meant the ball sails 40 yards up and 40 down, IF vertically up, then vertically down, the ball is always above the 35 yard line.

if the ball is punted at an angle, and 40 means not a horizontal distance but following the curvature of a parabola, then the ball is above anywhere from the home team's 35 yard line to the 45 yard line of the opposing team. You can't determine where with just the given information. So odds are the problem intended to mean 40 yards was the horizontal distance the ball traveled before it hit the ground. so, the answer you want is probably 45 yard line of the opposing team.

BUT then the 15 yard maximum height becomes irrelevant.

so construct the parabolic equation using 15 as the max height

general parabolic formula is

h(t) -16t^2 + vot + vo ho=0 h0, vo = iniital velocity, how hard the ball is punted

v(t) = h'(t) = -32t + ho = 0

t=vo/32 seconds at max height

max h(ho/32) = 15 = -16(vo/32)^2 + vo(vo/32) - 0 = 0

-16(vo^2)/32^2 + vo^2/32 = 15

vo^2/32 - vo^2/64 = 15

2vo^2 -vo^2 = 15

vo^2 = 15

vo = sqr15 feet per second = initial velocity when the ball is first kicked

t=vo/32 = sqr15/32 = time at maximum height

t = sqr15/16 = time when it hits the ground

and use the integral formula for calculating the length of a curve, integral of square root of (1-f'(x)), then

calculate the