A golfer imparts a speed of 27.4 m/s to a ball, and it travels the maximum possible distance before landing on the green. The tee and the green are at the same elevation. (a) How much time does the ball spend in the air? (b) What is the longest "hole in one" that the golfer can make, if the ball does not roll when it hits the green?
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Launch angle = 45 degrees from horizontal for max. range.
Vertical initial velocity component = (sin 45) x 27.4, = 19.375m/sec.
Horizontal component will be identical (sine and cosine of 45 are the same).
Time to max. height = (v/g) = 19.375/9.8, = 1.977 secs. (Use initial vertical component).
a) Time in air = (1.977 x 2) = 3.954 secs.
b) Longest hole in one = (3.954 x 19.375) = 76.61 metres (use horizontal velocity component).
Vertical initial velocity component = (sin 45) x 27.4, = 19.375m/sec.
Horizontal component will be identical (sine and cosine of 45 are the same).
Time to max. height = (v/g) = 19.375/9.8, = 1.977 secs. (Use initial vertical component).
a) Time in air = (1.977 x 2) = 3.954 secs.
b) Longest hole in one = (3.954 x 19.375) = 76.61 metres (use horizontal velocity component).