The initial velocity of a projectile is given by u = (6 i + 8 j ) m s ⁻¹ , where i is along the horizontal and j is along the vertical direction. What is the speed of the projectile at its maximum height?

Step-by-step solution

In projectile motion, the horizontal component of velocity remains constant throughout the flight, while the vertical component changes due to gravity. Given the initial velocity vector u = 6 i + 8 j , the horizontal component is u_x = 6 m s ⁻¹ and the vertical component is u_y = 8 m s ⁻¹ . At the maximum height, the vertical component of velocity becomes zero ( v_y = 0 ). Therefore, the velocity at the maximum height is entirely horizontal: v = 6 i m s ⁻¹ . The speed at the maximum height is the magnitude of this