Question

A golfer on a level fairway hits a ball at an angle of 42* to the horizontal that travels 100 yd before striking the ground. He then hits another ball from the same spot with the same speed, but at a different angle. This ball also travels 100 yd. At what angle was the second ball hit? (Neglect air resistance.)

Answer 1

Oh my, I suppose I will use feet and inches and miles and pounds and g = 32 ft/s^2
s = speed in ft/s
u = horizontal speed = s cos 42 = .743 s
Vi = s sin 42 = .669 s
t = time rising
2 t = time in air
300 feet = 2u t = 1.49 s t
v = Vi - 32 t
0 = .669 s - 32 t
t = .0209 s
so
300 = 1.49 s (.0209)s = .03115 s^2
s = 98.1 feet/second

now the second half

u = 98.1 cos T
Vi = 98.1 sin T
t is time rising again
300 feet = 2 u t = 196 cos T * t
0 = 98.1 sin T - 32 t
t = 3.07 sin T
so
300 = 196 cos T * 3.07 sin T
300 = 601 cos T sinT
cos T sin T = .499
2 sin T cos T = .998 = sin 2 T
so
2T = sin^-1 .998 = 86.7 deg
so
T = 43.3 deg

I suspect an arithmetic error because max range is at T = 45 degrees. the result should be as much above 45 as the original was below so It should have come out around 48 degrees.

Answer 2

A golfer on a level fairway hits a ball at an angle of 42* to the horizontal that travels 100 yd before striking the ground. He then hits another ball from the same spot with the same speed, but at a different angle. This ball also travels 100 yd. At what angle was the second ball hit? (Neglect air resistance.)

Answer 3

A golfer on a level fairway hits a ball at an angle of 39° to the horizontal that travels 86 yd before striking the ground. He then hits another ball from the same spot with the same speed, but at a different angle. This ball also travels 86 d. At what angle was the second ball hit? (Neglect air resistance.)

Answer 4

A golfer on a level fairway hits a ball at an angle of 23° to the horizontal that travels 104 yd before striking the ground. He then hits another ball from the same spot with the same speed, but at a different angle. This ball also travels 104 yd. At what angle was the second ball hit? (Neglect air resistance.)