Question

1. a kicked soccer ball has an initial velocity of 25 meters per second at an angle of 40° above the horizontal, level ground. what is the vertical component of initial velocity
2. calculate the maximum height the ball reaches above its initial position.

Explanation:

Step1: List known values

Initial vertical velocity $v_{iy} = \sin(40^\circ) \times 25 \approx 16.07\ \text{m/s}$, final vertical velocity at max height $v_{fy} = 0\ \text{m/s}$, acceleration $a = -9.8\ \text{m/s}^2$

Step2: Use kinematic equation

$$v_{fy}^2 = v_{iy}^2 + 2ah$$
Rearrange to solve for $h$:
$$h = \frac{v_{fy}^2 - v_{iy}^2}{2a}$$

Step3: Substitute values

$$h = \frac{0^2 - (16.07)^2}{2\times(-9.8)}$$
$$h = \frac{-258.24}{-19.6} \approx 13.17$$

Answer:

$\approx 13.2\ \text{meters}$ (or $\approx 13.17\ \text{meters}$)