Finding the Angle of a Projectile Launched from a Cliff

[alfredo24pr]

Homework Statement

A catapult on a cliff launches a large round rock towards a ship on the ocean below. The rock leaves the catapult from a height H of 34.0 m above sea level, directed at an angle θ above the horizontal with an unknown speed v0.

The projectile remains in flight for 6.00 seconds and travels a horizontal distance D of 149.0 m. Assuming that air friction can be neglected, calculate the value of the angle θ.

Homework Equations

y=y0 + v0yt - 0.5gt^2

tan θ = y/x

The Attempt at a Solution

I used y=y0 + v0yt - 0.5gt^2

y= -34 + 0 + 0.5 (9.8) (6^2)
y= -34 + 4.9(36)
y= -34 + 176.4
y= 142.4m

For x, the distance is given: 149 m

The angle:
tan θ = y/x
tan θ = 142.4/149
θ = 43.7

Is that correct? LONCAPA does not accept my answer, so if it is right I will assume that it is the degrees unit.

 

[rl.bhat]

In the first equation in your solution, voy is not equal to zero.

 

[alfredo24pr]

how do I find it?

 

[rl.bhat]

I used y=y0 + v0yt - 0.5gt^2

The above equation becomes
y=y0 + v0*sin(theta)*t - 0.5gt^2
Find voy*sin(theta). From second equation, you know vo*cos(theta). Now proceed.

 

[verty]

I think this is a very difficult question. You need to use two s-formulas:

s_x = ...
s_y = ...

For time t = 6, you get two equations in v_0 and theta.

 

[alfredo24pr]

Please post some calculations, because I have tried different ways and still have not found the correct answer.

 

[rl.bhat]

y=y0 + v0yt - 0.5gt^2

y= -34 + vo*cos(theta)*6 + 0.5 (9.8) (6^2)

Find cos(theta)

 

[alfredo24pr]

y=y0 + v0yt - 0.5gt^2

y= -34 + vo*cos(theta)*6 + 0.5 (9.8) (6^2)

Find cos(theta)

now i have to unknows..y and the angle. Now what?

 

[rl.bhat]

now i have to unknows..y and the angle. Now what?

When the rock reacxhes the ocean, displacement is zero. Hence y = o.

 

[alfredo24pr]

When the rock reacxhes the ocean, displacement is zero. Hence y = o.

and what is the angle? I am missing the vo and thetha.
Please help me more detailed because my professor confused me more when I asked him about this

 

[rl.bhat]

0 = -34 + vo*cos(theta)*6 + 0.5 (9.8) (6^2)
Find vo*cos(theta)
x = vo*sin(theta)*t.
Substitute the values of x and t. Find vo*sin(theta).
From these two values find vo and theta.

 

[verty]

I think rl.bhat has made it perfectly clear what to do. You've been helped, Alfredo.

 

[alfredo24pr]

my answer was correct, it was the lon capa that did not accept my units. Thanks anyway :)