a golf player hits a ball and the ball leaves the ground with an initial speed v

Question

a golf player hits a ball and the ball leaves the ground with an initial speed v0=22 m/s at an angle of 61 degree above the horizontal. the player hopes that the ball will fly over a tree that has a height h=16 m and is located at distance d=39 m in front of the player, as shown in the figure

a) find the greatest vertical height above the ground that the golf ball can reach

b) unfortunately, the golf ball hits the tree. find the height of the ball, as measured from the ground, when it hits the tree

Explanation / Answer

given that

initial speed v0 = 22 m/s

theta = 61 degrees

h = 16 m

d = 39 m

a) from the relation

maximum height H = v0^2sin^2(theta)/2g

H = 22^2sin^2(61)/2*10 = 18.51 m

b) y-y0 = usin(61)*t-1/2gt^2

x-x0 = 39 = ucos(61)t

t = 39/22cos61 = 3.66 sec

16-y0 = 22sin61*3.66-1/2*10*3.66^2

16-y0 = 70.42-66.98 = 3.44

y0 = 16-3.44

y0 = 12.56 m

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