A football is kicked from ground level with an initial velocity of 23.0 m/s at angle of 45.0° above the horizontal. How long is the football in the air before it hits the ground? Ignore air resistance.
Since the ball travels up and eventually comes back down to the same level, the vertical distance y traveled by the football is zero. So y = 0
Find the vertical velocity of the football. The ball has both a horizontal and a vertical velocity. We're interested in the initial vertical velocity, i.e., the speed of the ball immediately after it is kicked. Call this viy
viy = 23.0m/s * sin 45 = 23 * .707 = 16.26 m/s
Now use the kinematic equation d = vit + 0.5*(a*t2)
The distance d is just the vertical distance y, which is zero. Substituting:
0 = 16.26*t + 0.5* (-9.8* t2)
Need to solve for t, which is the time the football is in the air
0 = t(16.26 - 4.9t)
Divide both sides by t, and so 0 = 16.26 - 4.9t
now solve for t.
16.26 = 4.9t
16.26/4.9 = t
t = 3.32 seconds
The football is in the air for 3.32 seconds before it hits the ground.