What Is the Optimal Angle to Hit a 5m High Target with a 60 m/s Projectile?

[curiosity colour]

Homework Statement

A projectile is fired with a velocity of 60 m per second at an angle, theta, from a horizontal ground towards the roof of a tunnel of height 5m. If the projectile just barely touches the roof, determine the
a) angle of projection
b) time of the flight
c) range of the projectile

Homework Equations

2-Dimensional Equations [/B]

The Attempt at a Solution

s
I had tried to find it by finding the velocity Y componet first, using v square=u square +2as, after i found it, I use tan theta= y/x, and the answer came out were wrong. And now i have no clue how to do it, please help me[/B]

 

[Merlin3189]

Your method sounds right. Perhaps you could show the detail so that we can check your calculations?

Edit: though now I do it myself, your tan(θ)=y/x looks suspicious.
After you've found Y, the vertical speed, what do you do next?

 

[Nidum]

The projectile will follow a curved path - not a straight line .

Have a look at the way this problem was solved . You can use similar methods to solve your problem .

 

[curiosity colour]

Your method sounds right. Perhaps you could show the detail so that we can check your calculations?

Edit: though now I do it myself, your tan(θ)=y/x looks suspicious.
After you've found Y, the vertical speed, what do you do next?

yes, you're correct. After you point it out, I look over my drawing, and found out i put the initial velocity at wrong axis(x axis), which should be at the z axis. Now i redraw it, I'm believe this is right. And now i redo it with sin (θ)=y/z, I'm still getting the wrong answer.
https://goo.gl/photos/9CtTGndLvumqJPPEA
Edit: it's seem my picture is not displaying, I'm looking into it.

 

[physics user1]

Consider the y-axis first

It says that the object barely touches the roof, that means that the maximum height is 5 m
Also at the maximum height the y component of the velocity is 0

Set the two equations of kinematics on the y-axis with those information, you should get a system of two equations with variables the angle theta and the time

 

[curiosity colour]

Consider the y-axis first

It says that the object barely touches the roof, that means that the maximum height is 5 m
Also at the maximum height the y component of the velocity is 0

Set the two equations of kinematics on the y-axis with those information, you should get a system of two equations with variables the angle theta and the time

thx! I got the answer