a) c) d) A projectile is launched from the back of a cart as shown below. Its initial velocity is vy at an angle 6 above horizontal, and it lands at Point P. Assume that the initial height of the projectile 1s small enough that it can be considered ground level. Express all algebraic answers in terms of the given variables and fundamental constants. " Derive an expression for the time it takes for the projectile to reach Point P, % Now, assume that at the moment of the launch, the cart was traveling to the right at a speed of v,, as shown above. It lands at Point Q, which is half the distance from the launch spot at Point P. Derive an expression for v; in terms of the other given vanables. After the launch, the cart experiences a braking force of F = -bv, where b is a constant and v is the speed of the cart. Derive an expression for the speed of the cart as a function of time. How far will the cart travel before coming to a stop