Projectile Motion from a height

In summary, the problem involves a projectile being shot at a 35 degree angle from a height of 900 m and landing vertically 2500 m away. The initial velocity of the launch can be solved for using the kinematic equations and setting up equations for motion in both the x and y directions. The quadratic formula can then be used to solve for the time of flight, which can be used to find the initial velocity. Trigonometry may also be used in the kinematic equations to solve for the initial velocity.
  • #1
rachie9
7
0
A projectile is shot at a 35 degree angle from a height of 900 m. The it lands 2500 m away vertically. What was the initial velocity of the launch?



I do not know what relevant equations to use- I've tried using the integrals of position vectors like Vox(t) = 2500 m and Voz(t) - 1/2 gt^2 = 900 m, but I don't know how to solve this without knowing the time of flight.
 
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  • #2
You can do this without calculus.

HINT:

Use the kinematic equations and set up equations the motion in both the x and y directions. This should give you enough equations to eliminate time from the problem and solve for the initial velocity.
 
  • #3
Do I use the kinematic equations Vo= at and x= .5Vo(t)?
 
  • #4
Since I'm given an angle, I feel like I should be using trig. Is there some way I can involve trig in the kinematic equations?
 
  • #5
OK, I have figured out what I need to do, but need help with the math!

I need to solve for t in the 2 eqs: 2500 = Vocos35t and 900 = (Vosin35 - 4.9t)(t) and then set the equations equal to solve for Vo. But in the second equation, how do I solve for t?!
 
  • #6
In the second equation you have a quadratic (Bring all terms to one side of the equation). You need to use the quadratic formula to solve for t.
 
Last edited:

1. What is projectile motion from a height?

Projectile motion from a height refers to the curved motion of an object that is launched at an angle from a certain height above the ground. This motion is a combination of horizontal and vertical components, and is affected by gravity.

2. How is the trajectory of a projectile affected by its initial velocity?

The initial velocity of a projectile, which includes its speed and direction, determines the shape and range of its trajectory. A higher initial velocity results in a longer range and a flatter trajectory, while a lower initial velocity results in a shorter range and a steeper trajectory.

3. What is the impact of air resistance on projectile motion from a height?

Air resistance, also known as drag, can affect projectile motion from a height by slowing down the object's horizontal and vertical velocities. This results in a shorter range and a lower maximum height than if there was no air resistance present.

4. How does the angle of launch affect the trajectory of a projectile?

The angle of launch, also known as the angle of elevation, is the angle at which the projectile is launched from a horizontal surface. Changing this angle can greatly affect the range and height of the projectile, with a 45 degree angle typically resulting in the maximum range.

5. Can the initial height of a projectile affect its trajectory?

Yes, the initial height from which a projectile is launched can greatly affect its trajectory. A higher initial height will result in a longer flight time and a longer range, while a lower initial height will result in a shorter flight time and a shorter range.

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