Question

if a launch angle of 32 degrees can reach a hole but a tree is in the way, what angle can be used to lob a golf ball over the tree to the hole?

Answer 1

we know, for a given initial speed, for angles theta and (90-theta) the horizontal range is same.

so, the angle can be used = 90 - 32

= 58 degrees <<<<<<<<<<<<----------------------------------------------Answer

we know, Range R = vo^2*sin(2*theta)/g

when angle of projection = 90 - theta

Range = vo^2*sin(2*(90 - theta))/g

= vo^2*sin(180 - 2*theta)/g

= vo^2*sin(2*theta)/g   (since sin(180 - 2*theta) = sin(2*theta))

so, for the angles theta and (90 - theta) the range is same.