1. * A projectile is shot from a launcher at an angle e, with an initial velocity magnitude v., from a point even with a tabletop. The projectile lands on the tabletop a horizontal distance R (the "range") away from where it left the launcher. Set this up as a formal problem, and solve for vo (i.e., determine an expression for Vo in terms of only R, 0., and g). Your final equation will be called Equation 1.

2. A projectile is shot from a launcher at an angle 0,, with an initial velocity magnitude vo, from a point even with a tabletop. The projectile hits an apple atop a child's noggin (see Figure 1). The apple is a height y above the tabletop, and a horizontal distance x from the launcher. Set this up as a formal problem, and solve for x. That is, determine an expression for x in terms of only v₁, o,y and g. Actually, this is quite a long expression. So, if you want, you can determine an expression for x in terms of v., 0., and time t, and determine another expression for timet (in terms of v., 0., y and g) that you will solve and then substitute the value of t into the expression for x. Your final equation(s) will be called Equation 3 (and Equation 4).

4.56 ... CALC An object of mass m is at rest in equilibrium at the origin. At t = 0 a new force F(t) is applied that has components Fx(t) = k₁ + k₂y Fy(t) = k3t where k₁, k2, and k3 are constants. Calculate the position (1) and veloc- ity (t) vectors as functions of time.