A football is kicked at ground level with a speed of 15.4 m/s at an angle of 34.7° to the horizontal. How much later does it hit the ground?
(in s)
Vo = 15.4m/s[34.7o]
Xo = 15.4*Cos34.7 = 12.7 m/s.
Yo = 15.4*sin34.7 = 8.77 m/s.
Y = Yo + g*Tr = 0 @ max.ht.
8.77 - 9.8*Tr = 0
-9.8Tr = -8.77
Tr = 0.895 s. = Rise time.
Tf = Tr = 0.895 s. = Fall time.
Tr+Tf = 0.895 + 0.895 = 1.79 s. to hit
gnd.
To find out how much later the football hits the ground, we need to consider its motion along the vertical direction. We can use the kinematic equations of motion to solve for the time it takes for the football to hit the ground.
First, let's break down the initial velocity of the football into its vertical and horizontal components. The vertical component can be found using the formula:
Vy = V * sin(θ)
Where:
Vy is the vertical component of the velocity
V is the initial velocity (15.4 m/s)
θ is the angle of launch (34.7°)
So, Vy = 15.4 m/s * sin(34.7°)
Next, we can calculate the time it takes for the football to reach the ground using the following equation:
t = (2 * Vy) / g
Where:
t is the time taken to hit the ground
Vy is the vertical component of the velocity
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Now we can substitute the values and solve for t:
t = (2 * Vy) / g
t = (2 * 15.4 m/s * sin(34.7°)) / 9.8 m/s^2
t ≈ 1.83 seconds
Therefore, the football hits the ground approximately 1.83 seconds later.