A Football is kicked 66.6 meters in 5.39 seconds. What was the initial velocity?

Magnitude and Direction

L=vₒ²•sin2α/g = 66.6

t= 2vₒ•sinα/g = 5.39
vₒ = t•g/2•sinα
L=vₒ²•sin2α/g= t²•g²•2•sinα•cosα/g•4•sin²α= t²•g/2•tanα
tanα = t²•g/2•L
α= arctan t²•g/2•L = arctan (5.39²•9.8/2•66.6)=64.9°.
vₒ = t•g/2•sinα=5.39•9.8/2•sin 64.9°=...

I am not comin up with the same answers

To find the initial velocity of the football, we can use the equation of motion:

v = u + at

where:
v is the final velocity (which is zero when the ball reaches its maximum height),
u is the initial velocity we're trying to find,
a is the acceleration (which is the acceleration due to gravity, g),
and t is the time interval (in this case, the time of flight, which is 5.39 seconds).

First, let's calculate the acceleration due to gravity, which is approximately 9.8 m/s^2.

Now, we can rearrange the equation to solve for u:

u = v - at

Since the final velocity is zero (as the ball reaches its maximum height and starts to fall back to the ground), the equation becomes:

u = -at

Substituting the values:

u = -9.8 m/s^2 * 5.39 s

Now, let's calculate:

u = -52.862 m/s

The negative sign indicates that the initial velocity is in the opposite direction of motion. So, the magnitude of the initial velocity is 52.862 m/s, and the direction is opposite to the direction of motion.