Question

A very angry bird is desperate to destroy the very last evil piggy! The sling shot has been pulled to fixed position (the magnitude of the initial velocity is |v_0| = 10 m/s), and you can only adjust the projectile angle theta. Assume the motion is only subject to gravity; the piggy is located at coordinates (1m, -10cm) and the starting location for the bird is (0, 0). Determine the analytical function that relates the projectile angle theta and distance from the sling shot at the ground level. Calculate the projectile angle so that the bird can execute a direct hit on the piggy.

Answer 1

x-x0 = uxt+1/2axt^2

ux = ucostheta

ax = 0

x-x0 = ucostheta*t

x = ucostheta*t

t = 1/10costheta

x0 = y0 = 0

x = 1m

y = -0.1 m

y = usintheat*t-1/2gt^2

-0.1 = 10sintheta*1/10costheta-4.9/100cos^2theta

0.049cosec^2theta-tan(theta) = 0.1