In a lecture demonstration, the instructor aims a blowgun directly at Barney, a stuffed purple dinosaur, who is suspended from the ceiling at a vertical height H above the muzzle of the blowgun, a horizontal distance D away. At the instant she launches a dart with speed v0, Barney is released from rest.

a. Derive an expression, in terms of system parameters, for the dart’s vertical position when the dart has covered the horizontal distance D. b. Derive an expression, in terms of system parameters, for Barney’s vertical position at the instant the dart has the covered the horizontal distance D. Hint: The angle θ between initial velocity and the horizontal is not given, but you can find sin θ, cos θ and tan θ from the given distances.