A projectile is launched from the top of a tower of positive height h with speed u at an angle θ above the horizontal.At the instant the projectile reaches its highest point, its horizontal distance from the launch point is exactly half of its final horizontal range on the ground. Which statement is correct?
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Question

A projectile is launched from the top of a tower of positive height h with speed u at an angle θ above the horizontal.At the instant the projectile reaches its highest point, its horizontal distance from the launch point is exactly half of its final horizontal range on the ground. Which statement is correct?

Options

G1 Physics · Accepted Answer

Time to reach highest point: t H t_H t H ​ = u sinθ/g. Horizontal distance to highest point: x H x_H x H ​ = u cosθ· t H . t_H. t H ​ . If x H x_H x H ​ is half the final range R, x H x_H x H ​ = R/2. Since horizontal velocity is constant, R = u cosθ·T, where T is total time of flight. Thus, u cosθ· t H t_H t H ​ = ½u cosθ·T ⇒ T = 2 t H t_H t H ​ = 2u sinθ/g. But this is exactly the time at which a projectile returns to its launch height. For a tower of positive height h, the ground is below th…