A body is projected with an initial velocity U at an angle O to the horizontal. The time taken by it to reach its maximum height is given by the expression

When a projectile is projected with an initial velocity U at an angle O to the horizontal, it follows a parabolic path. The projectile reaches the maximum height at a certain point, then falls back to the ground. At the highest point, the vertical component of the velocity becomes zero. Let's assume that the time taken by the body to reach the maximum height is t. At the maximum height, the vertical component of the velocity becomes zero. Therefore, using the first equation of motion: v = u + gt where v = 0 and u = Usinθ 0 = Usinθ - gt gt = Usinθ t = Usinθ/g Therefore, the time taken by the body to reach its maximum height is given by the expression: t = Usinθ/g Thus, the correct option is: \(\frac{u \text{sin}\theta}{g}\)