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.

4.14 ⚫ A 2.75 kg cat moves in a straight line (the x-axis). Figure E4.14 shows a graph of the x- component of this cat's velocity as a function of time. (a) Find the maximum net force on this cat. When does this force occur? (b) When is the net force on the cat equal to zero? (c) What is the net force at time 8.5 s? Figure E4.14 V₁ (m/s) 12.0 10.0 8.0 6.0 4.0 2.0 0 t(s) 2.0 4.0 6.0 8.0 10.0