y v,t (x, y) Figure 4.9 The position vector r, of a projectile launched from the origin whose initial velocity at the origin is v,, The vector v,t would be the displacement of the projectile if gravity were absent, and the vector gt? is its vertical displacement from a straight-line path due to its downward gravita- tional acceleration.

sketch the vectors A= -3i+j and B=i+3j [i.e (-3,1) and (1,3). what propety do they share ]

A football kicker can give the ball an initial speed of 25.0 m/s. What are the (a) least and (b) greatest elevation angles at which he can kick the ball to score a field goal from a point 50.0 m in front of goalposts whose horizontal bar is 3.44 m above the ground? When doing this, you may want to research some trig identities to get a formula involving only tangent functions. Also, since there are two values of angle that will work, maybe the quadratic formula is involved.

Question 2. A projectile is fired from the ground with an initial speed v at an angle 0 above the horizontal. (a) At t = 0, what is the velocity vector? (b) At what time t' does the projectile reach its maximum height? (c) What is the velocity vector at the top of the trajectory? (d) What is the horizontal distance traveled by the projectile? (e) At what angle should one launch the projectile to maximize horizontal distance traveled?