20 POINTS
If a football is kicked in the air from the ground, and it takes 2 seconds to reach a height of 94 feet, what was the initial vertical velocity of the football?

Step-by-step explanation:

The formula for projectile motion in this case where we're dealing the "American" measure of gravity in feet per second squared, is

 where s(t) is the height of the object after a certain amount of time has gone by, v₀ is the initial vertical velocity (our unknown in this case), and h₀ is the initial height.

For us, the initial height is 0 because the ball started off on the ground.  What we are being asked is what is v₀, when after 2 seconds have gone by and the ball is 94 feet in the air.  94 feet in the air is the position of the ball, s(t) after t seconds go by.  What we are being asked to find then, is v₀ when s(2) = 94

which simplifies to

94 = -64 + 2v₀ and

158 = 2v₀ so

v₀ = 79 feet per second

79 feet/sec

Step-by-step explanation:

s = ut + ½at²

a = -32

s = 94

t = 2

94 = 2u -16(2)²

2u = 158

u = 79

54

step-by-step explanation: