Calculating Launch Angle of Rock from Catapult on a Cliff

In summary: What is the height of the rock then?In summary, the rock is launched from a catapult and rises to a height of 32 meters above sea level, before falling into the ocean below.
  • #1
BMWPower06
92
0

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 32.0 m above sea level, directed at an angle q above the horizontal with an unknown speed v0.
http://img230.imageshack.us/img230/5669/cliffvl5.gif [Broken]
The projectile remains in flight for 6.00 seconds and travels a horizontal distance D of 158.0 m. Assuming that air friction can be neglected, calculate the value of the angle q.


Calculate the speed at which the rock is launched.


Homework Equations


X = Xo+ Vot+.5at^2

V=Vo+at

V^2= Vo^2 + 2a (X-Xo)


The Attempt at a Solution



So i drew a FBD and got:
Xo= 0
X= 158 m
Yo= 32m
Y= 0
a= -9.8 m/s^2

i tried to use the X=Xo... equation but I am not sure what to do with theta. In other words, what does theta equal in this equation? i know its going to be Xsin/cos theta, but don't know what to do.

Thanks
 
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  • #2
You know how long the object was in flight. You also know the horizontal distance traveled in that amount of time. Thus, you are essentially given the horizontal component of the velocity. Now, your only task is to determine the initial vertical component of the velocity. Afterwards, vector addition will reveal the initial velocity.

If you treat the two components (horizontal and vertical) separately, the vertical component can easily be found by using the famous kinematic equations for constant acceleration.

After you know the initial velocity, use trigonometry to quickly find the launch angle.
 
  • #3
CaptainZappo said:
You know how long the object was in flight. You also know the horizontal distance traveled in that amount of time. Thus, you are essentially given the horizontal component of the velocity. Now, your only task is to determine the initial vertical component of the velocity. Afterwards, vector addition will reveal the initial velocity.

If you treat the two components (horizontal and vertical) separately, the vertical component can easily be found by using the famous kinematic equations for constant acceleration.

After you know the initial velocity, use trigonometry to quickly find the launch angle.
ok so i got:

Theta: 4.25×101 deg

Calculate the speed at which the rock is launched.
3.57×101 m/s

To what height above sea level does the rock rise?
How do i find the height now?
 
  • #4
Pretend your catapult is on level ground. How high then does the rock reach? Now, hollow out the ground below that point and stick in the ocean 32m below the ground level.
 

1. How do you calculate the launch angle of a rock from a catapult on a cliff?

The launch angle can be calculated using the following equation: launch angle = arctan((2 * height difference) / distance), where the height difference is the vertical distance between the catapult and the cliff edge, and the distance is the horizontal distance between the catapult and the point where the rock lands.

2. What factors influence the launch angle of a rock from a catapult on a cliff?

The launch angle is influenced by the height difference between the catapult and the cliff, the distance between the catapult and the point where the rock lands, and the initial velocity of the rock from the catapult.

3. Can the launch angle be adjusted to achieve a longer distance for the rock?

Yes, adjusting the launch angle can help increase the distance of the rock. Generally, a higher launch angle will result in a longer distance, but there is a maximum angle that should not be exceeded, as it may cause the rock to fall short or even backfire towards the catapult.

4. How can the launch angle affect the trajectory of the rock?

The launch angle affects the trajectory of the rock by determining the initial direction and angle at which the rock is launched. A higher launch angle will result in a steeper trajectory, while a lower launch angle will result in a flatter trajectory.

5. Are there any other factors that should be considered when calculating the launch angle of a rock from a catapult on a cliff?

Other factors that should be considered include the weight and shape of the rock, air resistance, and wind direction. These factors may affect the accuracy of the calculated launch angle and should be taken into account for more precise results.

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