Kinematics Horizontal Motion Problem

Question

A projectile is fired at 28 m/s at an angle of 33 degrees with the horizontal from a point 75 m above the ground. How long did it take for the projectile to hit the ground below? How far did the projectile travel horizontally?

Answer 1

I'm assuming the projectile is fired upwards at 33°, and I use a = -g = -9.8 m/s². From Δy = v_ot + 1/2 at², -75 = (28 sin 33) t - 4.9 t² which yields 4.9 t² - 15.25 t - 75 = 0. Quadratic formula, adopting the positive root to get a time after launch, yields t = (15.25 + 41.26)/9.8 = 5.77 s (5.8 s to 2 sig figs).

Distance traveled horizontally Δx = v_x t = (28 cos 33) t = 135 m (140 m to 2 sig figs).