A golfer impacts a speed of 38.7 m/s to a ball, and it travels the maximum possi
ID: 1415412 • Letter: A
Question
A golfer impacts a speed of 38.7 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, it the ball does not roll when it hits the green? A golfer impacts a speed of 38.7 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, it the ball does not roll when it hits the green?Explanation / Answer
a)
max range occurs when theta = 45deg
so the time of flight comes from y = y0 + vy0 * t - 0.5 * g * t^2 where y = y0 = 0
and
vy0 = v0 * sin(45) = 38.7m/s*sin(45) = 27.4m/s
0 = 27.4 * t - 0.5 * g * t^2
t* (vy0 - 0.5 * g * t) = 0
therefore
t = 2 * vy0 / g = 2 * 27.4 / 9.8 = 5.58s
b)
the horizontal distance travled is vx0*t = v0 * cos(45) * t = 38.7 * cos(45) * 5.58s = 153m