What's the speed of the ball 1 second after it was kicked?

Homework Statement

A soccer ball is kicked with an initial horizontal velocity of 15m/s and an initial velocity of 16m/s.
What's the speed of the ball 1 second after it was kicked?

Homework Equations

Initial velocity = sqrt([horiz. Velocity]^2 + [vertical Velocity]^2)

Final velocity = initial velocity + (gravity*time)

The Attempt at a Solution

Initial velocity = sqrt (15^2 + 16^2)
Initial velocity = 22m/s

Final velocity = 22m/s + (9.81m/s*1second)
Final velocity = 31.81 m/s

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kuruman
Homework Helper
Gold Member
You are confusing velocity with speed. "Gravity*time" acts on the vertical component of the velocity only, not on the speed.

Speed is distance over time.
I calculated that the distance traveled by the ball is (22sin (2*46.8))/ 9.81 = 49.24 meters

So after one second that the ball was kicked, speed = 49.24m / 1 second = 49.24 m/s
This is still incorrect

Nathanael
Homework Helper
Speed is distance over time.
I calculated that the distance traveled by the ball is (22sin (2*46.8))/ 9.81 = 49.24 meters

So after one second that the ball was kicked, speed = 49.24m / 1 second = 49.24 m/s
This is still incorrect

Please explain your work. For instance, what angle are you taking the sine of?

Also we don’t want the distance over time, that gives an average speed. We want the instantaneous speed, I would assume.

I got 46.8 degrees from using the initial horizontal velocity: 15m/s and the vertical velocity: 16m/s.
Theta = tan^-1 (16/15)
Theta = 46.8 degrees

Nathanael
Homework Helper
I got 46.8 degrees from using the initial horizontal velocity: 15m/s and the vertical velocity: 16m/s.
Theta = tan^-1 (16/15)
Theta = 46.8 degrees
Why arctangent? You said 16 m/s is the initial speed, not the vertical component.

Either way you don’t need to worry about angles. What is the vertical speed over time? What is the horizontal speed over time? So then what is each after one second?

CWatters
Homework Helper
Gold Member
Melina... In your attempt at a solution in #1 you are doing the vector addition to work out the speed too soon.

Try doing the vector addition after one second.

haruspex