9514 1404 393
Answer:
- 177 ft at 31°
- 198 ft at 49°
Step-by-step explanation:
The vertical height as a function of time for some initial velocity v and some launch angle α is ...
h = (-16t +v·sin(α))t
This will be zero (the ball hits the ground) at ...
t = v·sin(α)/16
__
The horizontal distance as a function of time is then ...
x = v ·cos(α)t
Where t is given from the height equation, the horizontal distance to the point where the ball hits the ground is ...
x = v·cos(α)·v·sin(α)/16 = v²·sin(2α)/32
For an angle of 31°, the ball will travel ...
(80 ft/s)²·sin(62°)/(32 ft/s²) = (200 ft)·sin(62°) ≈ 176.6 ft . . . at 31° angle
For an angle of 49°, the ball will travel ...
(200 ft)·sin(98°) ≈ 198.1 ft . . . at 49° angle
