Question

A footballer kicks a ball at an angle of 45 degrees with the horizontal. If the ball was in the air for 10 seconds and lands 4000 meter away, determine its initial speed

Answer 1

The horizontal distance for the projectile motion

$$L=v_0t\cos\theta.$$

Hence, the initial speed

$$v_0=\frac{L}{t\cos\theta}=\frac{4000}{10\cos45^{\circ}}=566\:\rm m/s.$$