Question regarding vertical velocity

[slu1986]

How do you calculate vertical velocity when you're not given an angle?

For example,
A player kicks a football at the start of the game. After a 6.6 second flight, the ball touches the ground 59 m from the kicking tee. If air resistance is disregarded, find.

a. The maximum height reached by the ball
b. the vertical component of velocity at kick-off
c. the horizontal component of velocity at kick-off

If someone could please explain to me how to solve for the variables when not given an angle. I would greatly appreciate it. Thanks

 

[cepheid]

You treat the angle as one of the unknowns in the problem. Also, since you know the range of the projectile (the horizontal distance spanned) and the time it took to span that distance, you know the horizontal component of velocity.

 

[slu1986]

So would the horizontal component of velocity be = 8.9 m/s
I am still so confused at how to solve the problem without having an angle.

 

[cepheid]

As I was saying, treat the angle as a variable. Call it theta or something. Then we know that:

$$v_{0x} = v_0 \cos{\theta} = 8.9\, \textrm{m/s}$$

$$v_{0y} = v_0 \sin{\theta}$$

So there are two unknowns, theta, and v0. But you have only one equation. You need two equations to solve for two unknowns. Where does the other piece of information come from? You know that the flight time is t = 6.6 s, and that this is projectile motion, which means that the ball experiences a constant acceleration equal to g. Therefore, the time to reach the max height is half that (3.3 s). Also, what can be considered the "final" velocity at this point is 0 m/s. So you know the final vertical velocity, the time, the acceleration...can you use this information to find the initial vertical velocity (hint: yes you can).