16 3. (25 pts.) A quarterback throws a football with an initial velocity of 23 m

Question

16 3. (25 pts.) A quarterback throws a football with an initial velocity of 23 m/s at an angle 40° with respect to the horizontal. The receiver awaits a distance Ar away dx (6 pts.) What are the horizontal (vox) and vertical (oy) components of the initial velocity? 2 b. (6 pts) If the receiver catches the football at the same height as it was throwg, how long does the ball spend on the air? 524: 310,US 19,6(DA) 4:98 (6 pts) If the receiver catches the football at the same height as it was thrown, how far is he from the quarterback (that is, find Ax)? o y /d/) (7 pts.) If the receivermisses the catch and another player located a distance d= 1.1 m below the launching height must his hands be behind tries to catch the football, h (in other words, what is the vetical position of the ball at that moment)?

Explanation / Answer

(a) Horizontal component of initial velocity, Vx = 23*cos40 = 17.62 m/s

Vertical component of initial velocity, Vy = 23*sin40 = 14.78 m/s

(b) Time to reach at the maximum height by the ball -

t = Vy/g = 14.78/9.81 = 1.51 s

So, the total time spend by the ball in the air, T = 2t = 2*1.51 = 3.02 s

(c) Horizontal range of the ball, x = Vx*T = 17.62*3.02 = 53.21 m

(d) Time taken by the ball to cover a distance of 1.1 m horizontally -

t = 1.1/17.62 = 0.062 s.

Vertical distance covered by the ball in this time -

h = Vy*t + (1/2)*g*t^2 = 14.78*0.062 + 0.5*9.81*0.062^2 = 0.935 m

So, the vertical position of the ball is 0.935 m below the height of the player.

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