Thrown Ball and Equilibrium

1. A putting green is located 420 m horizontally and 74.9 m vertically from the tee. What must be the magnitude and direction of the initial velocity if a ball leaving the tee is to strike this green after an elapsed time of 7 seconds?

2. A 10 m long, 300 N uniform pole is supported by hunter A at the left and and hunter B at the right end, with a 750 N deer hung at a point 3 m from the left end. determine the upward forces required by each hunter.

2. Let $\alpha$ be the initial angle of the speed with the horizontal axis x.

$Vx =V*cos(\alpha)$

$Vy = V*sin(\alpha)$

Now on the Y axis one has the eq

$H = Vy*t – g*t^2/2$

where t is the total time, and H the vertical distance to the green

Hence $Vy = (H+g*t^2/2)/t = (74.9+ 9.81*7*7/2)/7 = 45.035 m/s$

On the x axis one has the eq

$S = Vx*t$ where s is the horizontal distance to the green

$Vx = S/t = 420/7 = 60 m/s$

Now one has

$tan(\alpha) = sin(\alpha)/cos(\alpha) = Vy/Vx = 0.75$

$\alpha = 36.89 degree$

and $V = \sqrt(Vx^2+Vy^2) = 75.02 m/s$

5. There are two conditions that need to be fulfilled

Total force on is zero

$Fa+Fb-750-300 = 0$

Total rotational momentum on with respect to point b is zero.

$Fa*10 -750*(10-3) -300*10/2 =0$

$Fa*10 =750*7+300*5$

$Fa = 675 N$

From the first eq one has now

$Fb = 750+300-675 = 375 N$