Finding Initial Speed Given Range

In summary, the conversation discusses using a catapult to throw rocks and determining the necessary initial speed for the rocks to reach a maximum range of 0.67 km. The formula Rmax=V0^2/g is used to calculate the initial speed, with the understanding that the angle must be 45 degrees for maximum range. The importance of understanding the derivation of equations from velocity-time graphs is also emphasized.
  • #1
reigner617
28
0

Homework Statement


If you want to use a catapult to throw rocks, and the max range is 0.67 km, what initial speed must the rocks have as they leave the catapult?

Homework Equations



v=Δr/Δt

The Attempt at a Solution


I sketched a graph of the projectile trajectory with the desired range on the x-axis. I also converted 0.67 km to 670 m. I concluded that acceleration would be -9.8 m/s. I couldn't go any further since I feel like I am not given enough information to work with.
 
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  • #2
I feel like I am not given enough information to work with.
... you need to know the angle the stones are launched at - you are told this though. The way the question is written suggests you have already derived or had given to you a bunch of equations for range, max-height and so on. If not, then try sketching velocity-time graphs for the horizontal and vertical components of the motion.

note: the acceleration is -9.8m/s/s in the +y direction, taking +y to be "upwards".
 
  • #3
Thank you for the quick response. I used the formula Rmax=V02/g. After substituting the givens into the formula, I came up with 81 m/s
 
  • #4
Did you understand where the equation came from?
 
  • #5
Not quite, although a similar formula that I know is R=(V0^2)sin(2t)/g
 
  • #6
I also understand that for the range to be max, the angle has to be 45, and if we put 45 into the V0^2sin(2t)/g formula, sin2t would just be 1, and we are left with just V0^2/g
 
  • #7
reigner617 said:
Not quite, although a similar formula that I know is R=(V02)sin(2θ)/g ... I also understand that for the range to be max, the angle has to be 45, and if we put 45 into the V02sin(2t)/g formula, sin2θ would just be 1, and we are left with just V02/g
... well done :)

I just don't like the style of teaching that has students memorize a bunch of equations.
Note: that equation only works where the initial and final heights are the same - when you can derive the equations from velocity-time graphs you'll be able to do any ballistics problem, and many more besides, without having to memorize or look up any equations ... so it's a skill worth obtaining.
 

FAQ: Finding Initial Speed Given Range

1. How do I calculate initial speed given range?

To calculate initial speed given range, we can use the formula: initial speed = square root of (range x gravitational acceleration). This formula is derived from the equation of projectile motion, where range is equal to initial speed squared divided by gravitational acceleration. By rearranging the equation, we can solve for initial speed.

2. Can I use this formula for all types of projectiles?

Yes, this formula can be used for all types of projectiles as long as they are launched at an angle and the range is measured horizontally from the launch point. This formula assumes a constant gravitational acceleration, so it is not applicable for projectiles on other planets or in space.

3. What units should I use for range and initial speed?

For this formula, it is important to use consistent units. Range should be measured in meters (m) and initial speed should be in meters per second (m/s). This will ensure that the answer is in the correct unit of meters per second (m/s).

4. Is there a way to check my calculation?

Yes, there are several ways to check your calculation. One way is to use a projectile motion simulator or calculator, which can provide the initial speed given the range. You can also use algebra to rearrange the equation and solve for range using your calculated initial speed, and then compare it to the given range. If they are equal, then your calculation is most likely correct.

5. Are there any limitations to this formula?

Yes, there are a few limitations to this formula. As mentioned before, it assumes a constant gravitational acceleration and is not applicable for non-horizontal ranges or for projectiles on other planets or in space. It also does not take into account air resistance, which may affect the actual range of a projectile.

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