# Projectile Motion – Fired at ground level

A football is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the horizontal. Determine the time of flight, the horizontal displacement, and the peak height of the football ... Vi = Initial velocity
Vf = Final velocity
Vx = Horizontal velocity component
Vy = Vertical velocity component
a = Acceleration
t = time
H = Peak height
X = Horizontal displacement

For the horizontal components of motion, the equations are   Remember horizontal acceleration is always zero for this problem ( ax = 0). So we can rewrite above equations for horizontal motion as Equation (1) Equation (2)

For the vertical components of motion, the equations are Equation (3) Equation (4) Equation (5)

Apply equation (4) for vertical motion from point A to B Equation (4)

At the maximum height there are no vertical velocity, so it is zero Vfy = 0 To reach maximum height it takes only half of the full flight time   t = 3.28 s

Time of flight 3.28 seconds

Apply equation (1) for horizontal motion from point A to C Equation (1) X = 62.82 m
Horizontal displacement 62.82 meters.

Apply equation (5) for vertical motion from point A to B Equation (5)   Y = 13.17 m

Peak height 13.17 meters.