AP Physics 1 Projectile Motion Questions

Question

Alex the clown likes bouncing on very large trampolines. If Alex jumps on the trampoline and lands 15.0 meters away after 1.30 seconds, what was the initial angle he left the ground.

and

EvilKentevil is a daredevil. As part of his act, EvilKentevil gets into his cannon and shoots himself at a 25.0 degrees angle at an initial velocity of 30.0 m/s. How far away from his initial position does he land?

Answer 1

Alex: Final vertical velocity v_yf = v_yo + a t, and final = negative of initial when we ignore air resistance. So -v_yo = v_yo - (9.80 m/s²) (1.30 s), 2 v_yo = 12.7₄ [keep 4th digit to get 3 sig figs], and v_yo = 6.37 m/s. Δx = 1/2 (v_xo + v_xf) t, x component is constant, 15.0 m = v_x t and v_x = 11.5₄ m/s. Tan θ = v_yo / v_x = 0.552₁ and launch angle θ = 28.9°.

EvilKentevil: Given v_o = 30.0 m/s @ 25°, initial v_yo = 30.0 sin 25 = 12.6₈ m/s, v_x = 30.0 cos 25 = 27.1₉ m/s. From start to finish, Δy = 0 = v_yo t + 1/2 a t² = 12.6₈ t - 4.90 t² = t (12.6₈ -4.90 t) = 0, t = 12.6₈ / 4.90 = 2.58₇ s. Then Δx = v_x t = 70.4 m.