A soccer ball is kicked at 25m/s,35^circ above the horizontal.The player's foot makes contact with the ball 82 cm above the ground.What will be the ball's maximum height above the ground? 82cm

Here's how to calculate the maximum height of the soccer ball:<br /><br />**1. Break down the initial velocity into horizontal and vertical components:**<br /><br />* **Vertical component (Vy):** Vy = V * sin(angle) = 25 m/s * sin(35°) ≈ 14.34 m/s<br />* **Horizontal component (Vx):** Vx = V * cos(angle) = 25 m/s * cos(35°) ≈ 20.48 m/s<br /><br />**2. Calculate the time it takes to reach the maximum height:**<br /><br />At the maximum height, the vertical velocity becomes zero. We can use the following kinematic equation:<br /><br />Vfy = Voy + a*t<br /><br />Where:<br /><br />* Vfy = final vertical velocity (0 m/s at the peak)<br />* Voy = initial vertical velocity (14.34 m/s)<br />* a = acceleration due to gravity (-9.8 m/s²)<br />* t = time<br /><br />0 = 14.34 m/s + (-9.8 m/s²) * t<br />t = 14.34 m/s / 9.8 m/s² <br />t ≈ 1.46 s<br /><br />**3. Calculate the vertical displacement to reach the maximum height:**<br /><br />We can use another kinematic equation:<br /><br />Δy = Voy * t + 0.5 * a * t²<br /><br />Where:<br /><br />* Δy = vertical displacement<br />* Voy = initial vertical velocity (14.34 m/s)<br />* t = time (1.46 s)<br />* a = acceleration due to gravity (-9.8 m/s²)<br /><br />Δy = (14.34 m/s * 1.46 s) + 0.5 * (-9.8 m/s²) * (1.46 s)²<br />Δy ≈ 20.94 m - 10.44 m<br />Δy ≈ 10.5 m<br /><br />**4. Calculate the maximum height above the ground:**<br /><br />The initial height of the ball is 0.82 m (82 cm). Therefore, the maximum height above the ground is:<br /><br />Maximum height = Initial height + Vertical displacement<br />Maximum height = 0.82 m + 10.5 m<br />Maximum height ≈ 11.32 m<br /><br />**Therefore, the ball's maximum height above the ground will be approximately 11.32 meters.**<br />