The big deal with 2-dimensional kinematics is that we can break most problems ba

Question

The big deal with 2-dimensional kinematics is that we can break most problems back down into one dimensional problems if the acceleration is constant.

For example, vx = vx0 + axt where vx0 is the x component of the velocity at time t=0s, vx is the x component of the velocity at time t, and ax is the x component of the acceleration.

In the vertical direction, the same formula is valid for all of the y components: vy = vy0 + ayt where vy0 is the y component of the velocity at time t=0s, vy is the y component of the velocity at time t, and ay is the y component of the acceleration.

In projectile motion gravity is the only force acting on the ball. We will always choose the y-axis to be exactly vertical and in this case positive in the upward direction. Since gravity acts straight down, the x component of the acceleration will be 0 m/s2 and the y component of the acceleration will be -9.80 m/s2.

Consider the following case: you kick a ball. Just after it leaves your foot the x component of the velocity of the ball is 17.7 m/s and the y component of the velocity of the ball is 31.5 m/s.
After a time t=1.80 s, what is the x component of velocity of the ball?

After a time t=1.80 s, what is the y component of the velocity of the ball?

Explanation / Answer

a) Along the horizontal direction we have

vx = vx0 + ax t

Vx0 = 17.7 m/s

ax =0

=> Vx = 17.7 m/s

Along y direction

vy = vy0 + ay t

Vy0 = 31.5 m/s

ay = -9.8 m/ss

Vy = 31.5 - (9.8) (1.8)

=> Vy = 13.86 m/s

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