Physics Math

Question

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.

Answer 1

1. Acceleration a = -9.8 m/s²
2. Initial velocity vi = 23.0m/s
3. 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
4. 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 v_iy
1. v_iy = 23.0m/s * sin 45 = 23 * .707 = 16.26 m/s
5. Now use the kinematic equation d = v_it + 0.5*(a*t²)
6. The distance d is just the vertical distance y, which is zero.  Substituting:
1. 0 = 16.26*t + 0.5* (-9.8* t²)
2. Need to solve for t, which is the time the football is in the air
3. 0 = t(16.26 - 4.9t)
4. Divide both sides by t, and so 0 = 16.26 - 4.9t
5. now solve for t.
6. 16.26 = 4.9t
7. 16.26/4.9 = t
8. t = 3.32 seconds
7. The football is in the air for 3.32 seconds before it hits the ground.