Maximizing Golf Ball Distance and Hole in One: Intro Physics HW Help

[lolo]

hey everyone, i have a few questions that i just don't understand.
1) a golfer imparts a speed of 27.0m/s to a ball, it travels the max possible distance b4 landing on the green. the tee and the green are at the same level. a) how much time does the ball spend in the air? b) wat is the longest "hole in one" that the golfer can make, if the ball does not roll when it hits the ground?


i would really really appreciate ur help and if someone can do these problems can u please give clear solutions?
thanx alot

 

[Jameson]

I believe 45 degrees is the angle that produces the longest distance in projectile motion.

 

[Päällikkö]

a)
$$y = y_0 + v_{0y}t + \frac{1}{2}a_yt^2$$
$$x = x_0 + v_{0x}t + \frac{1}{2}a_xt^2$$
Both equations (especially the latter) reduce quite nicely with some logical thinking (what sort of velocity has an effect on the time?). Then just put the equations together and find the maximum (hint: derivate). Quickly done: 45 degrees does look like the correct answer. Now just throw the angle into the (reduced) equation you got in the first step.
Hint: Express $v_0$ in $v_{0y}$ and $v_{0x}$

b) You already got the equation you need in a). Now just throw the velocity in and you're done.

 

[DafreshDon]

a)
$$y = y_0 + v_{0y}t + \frac{1}{2}a_yt^2$$
$$x = x_0 + v_{0x}t + \frac{1}{2}a_xt^2$$
Both equations (especially the latter) reduce quite nicely with some logical thinking (what sort of velocity has an effect on the time?). Then just put the equations together and find the maximum (hint: derivate). Quickly done: 45 degrees does look like the correct answer. Now just throw the angle into the (reduced) equation you got in the first step.
Hint: Express $v_0$ in $v_{0y}$ and $v_{0x}$

b) You already got the equation you need in a). Now just throw the velocity in and you're done.

thanks that also just helped me

 

[DafreshDon]

but i simply used the equation for range to find longest
distance which is same as X, R=X= Vox*T,