The diagram above represents the trajectory of a projectile with an initial velocity U. Calculate the time taken to reach the maximum height. (Take g as acc...

To find the time taken to reach the maximum height, we need to use the fact that the vertical component of the velocity of the projectile at the maximum height is zero. This occurs when the projectile reaches the top of its trajectory. The initial vertical component of the velocity is Usin?. The vertical component of the velocity at the top of the trajectory is zero. Using the equation of motion for vertical motion, we can find the time taken to reach the maximum height. The equation of motion for vertical motion is given by: v = u + at where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. At the maximum height, the final velocity is zero, the initial velocity is Usin?, and the acceleration is the acceleration due to gravity, g. Therefore, we can write: 0 = Usin? - gt Rearranging this equation, we get: t = Usin? / g Therefore, the time taken to reach the maximum height is Usin? / g. The correct option is Usin? / g.