Pablo kicked a ball that went 12m/s at 14° from the ground to fly through the goalie's hands. How high did the ball go?​

Explanation:

There are a couple of things we need to clear up before we start the problem. First of all, we are given an angle in the problem along with an initial velocity. BUT this is what I call a "blanket" velocity: it is neither the upwards velocity nor is it the horizontal velocity. In order to find either the upwards velocity or the horizontal velocity we have to use either the sin or the cos function, respectively. Since we are working ONLY in the y-dimension, which is up and down, we use the sin function along with the given velocity to find the upwards velocity of the ball. Secondly, we have to know that the final velocity at the max height of the ball is 0. So here is what we have:

v₀ = 12sin14 so

v₀ = 2.9 m/s

a = -9.8 m/s/s

v = 0 m/s

Δx = ??? m

The equation we need is

v² = v₀² + 2aΔx and filling in:

0 = (2.9)² + 2(-9.8)Δx and

0 = 8.4 - 2.0 × 10¹Δx and

-8.4 = -2.0 × 10¹Δx so, to the correct number of sig dig,

Δx = 170 m

he kicked it 10 feet straight up into the air? i think this works.

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.