How Long Does a Particle Thrown at an Angle Travel Until It Lands?

[annalian]

Homework Statement

A particle is thrown in the angle pi/3 radian with speed 10m/S. Find the time of movement if the maximal height is equal to the distance of fall.

Homework Equations

v^2-voy^2=2gh

The Attempt at a Solution

0-10^2*3/4=2*10*hmax
hmax=3.75
v0x*2t=3.75
v0*cos60*2t=3.75
10*0.5*2*t=3.75
t=0.375. The answer in my book is 1S.
I also want to know why whe I use the formula of maximal height v0^2sin^a/2g and maximal fallL=v0^2sin2a/g with the data from the problem they don't come out to be equal.

 

[Jamison Lahman]

Homework Statement

A particle is thrown in the angle pi/3 radian with speed 10m/S. Find the time of movement if the maximal height is equal to the distance of fall.

Homework Equations

v^2-voy^2=2gh

The Attempt at a Solution

0-10^2*3/4=2*10*hmax
hmax=3.75
v0x*2t=3.75
v0*cos60*2t=3.75
10*0.5*2*t=3.75
t=0.375. The answer in my book is 1S.
I also want to know why whe I use the formula of maximal height v0^2sin^a/2g and maximal fallL=v0^2sin2a/g with the data from the problem they don't come out to be equal.

Can you explain what "time of movement" is? Is this the total time while the particle is in the air? What is the exact wording of the problem?

I am getting the same maximum height and using the equation $$ h = \frac{1}{2}at^2 $$ I am getting a total flight time of $\sqrt{3}$

 

[haruspex]

There seems to be too much information. That can be fixed by dropping the assumption that it lands at the same height it was launched at, but I still don't get the book answers.

 

[PhanthomJay]

The angle of pi/3 radians might be measured from the vertical axis.

 

[haruspex]

The angle of pi/3 radians might be measured from the vertical axis.

By dropping the assumption that it lands at the same height it was launched at, using pi/3 as angle to the horizontal I get a time of 1/4 s. Taking it as angle to the vertical makes it even less. To get a time of 1s I need a launch angle of acos(√2-1) to the horizontal, or about 65 degrees. That's using g=10m/s².

 

[PhanthomJay]

Poorly worded problem I can only assume it it is thrown at pi/3 radians with vertical on level ground. Vert comp of velocity thus 5 m/s. Rises to a height h then falls back vert distance h to ground, which is a 2nd assumption. Half sec up and half sec down. Problem should be tossed.

 

[haruspex]

Rises to a height h then falls back vert distance h to ground

Right, so it was just a confusing way of saying it lands back at the height it was thrown from. Well deduced.