A target starts from the origin at t = 0 and moves horizontally with constant speed 10 m/s. At the same instant, a projectile is fired from the same point with speed 20 m/s at an angle θ above the horizontal. The projectile is to hit the target when it returns to the ground level. Neglect air resistance. The required condition is:
Options

Question

A target starts from the origin at t = 0 and moves horizontally with constant speed 10 m/s. At the same instant, a projectile is fired from the same point with speed 20 m/s at an angle θ above the horizontal. The projectile is to hit the target when it returns to the ground level. Neglect air resistance. The required condition is:

Options

G1 Physics · Accepted Answer

For a non-zero meeting time, the horizontal positions must remain equal at the hit instant: projectile x = 20cosθ·t and target x = 10t. Thus 20cosθ = 10 ⇒ cosθ = 1/2. The projectile can then return to ground at t = 2u sinθ/g > 0. Therefore option A is correct.