Projectile Motion – Fired at ground level

Home Problems and Answers Classical Mechanics 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 ...

Projectile Motion
 
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
 
Equation for horizontal motionEquation for horizontal motionEquation for horizontal motion
 
Remember horizontal acceleration is always zero for this problem ( ax = 0). So we can rewrite above equations for horizontal motion as
 
Equation (1)
Equation (1)
Equation (2)
Equation (2)
 
For the vertical components of motion, the equations are
 
Equations for vertical motion
Equation (3)
Equations for vertical motion
Equation (4)
 
Equations for vertical motion
Equation (5)
 
Apply equation (4) for vertical motion from point A to B
 
Equations for vertical motion
Equation (4)
 
At the maximum height there are no vertical velocity, so it is zero Vfy = 0
 
Equations for vertical motion
 
To reach maximum height it takes only half of the full flight time
 
Equations for maximum height
 
Equations for maximum height
 
Flight time
 
t = 3.28 s
 
Time of flight 3.28 seconds
 
Apply equation (1) for horizontal motion from point A to C
 
Equations for horizontal motion
Equation (1)
 
Equations for horizontal motion
 
X = 62.82 m
Horizontal displacement 62.82 meters.
 
Apply equation (5) for vertical motion from point A to B
 
Equations for vertical motion
Equation (5)
 
Equations for vertical motion
 
Equations for vertical motion
 
Peak height
 
Y = 13.17 m
 
Peak height 13.17 meters.