Given range and angle - but not time - find initial velocity?

In summary, a missile with a 9500km range must have an initial velocity of km/h in order to travel that distance.
  • #1
exi
85
0

Homework Statement



Given a missile with 9500km range, what must its initial velocity be to travel that distance? Disregard issues introduced by the missile's boost phase, and state the velocity as km/h.

(Presumably, the curvature of the planet is to be ignored, as well.)

Homework Equations



Unsure; see below.

The Attempt at a Solution



If a missile is to have maximum range, then its launch angle ought to be 45°. It would also have a symmetrical trajectory and is affected by gravity at -9.8 m/s^2 (or 0.0098 km/s^2 in the terms of this problem).

The first thing that came to mind was to use R=Vo^2/g*sin(2*45) and solve for Vo, but that yielded something ridiculously slow for that long of travel.

I'm rather unsure as to which equation(s) ought to be used to solve such a problem, since everything I can find written in my notes refers to what appear to be slightly different situations.
 
Physics news on Phys.org
  • #2
exi said:
The first thing that came to mind was to use R=Vo^2/g*sin(2*45) and solve for Vo, but that yielded something ridiculously slow for that long of travel.
What did you get?
 
  • #3
Doc Al said:
What did you get?

I did it the first time without converting acceleration and had 300something km/h, or 186 mph.

The second time with the conversion worked out to like 93.1 km/h, which ... well, a 57 mph missile isn't going to travel 6,000 miles. :mad:
 
  • #4
You might want to redo your calculation--you're way off. Be sure you use standard units and then convert to km/h.
 
  • #5
Doc Al said:
You might want to redo your calculation--you're way off. Be sure you use standard units and then convert to km/h.

Yeah, so I am. 9.6488 km in a second sounds more like it (and is correct). Looks like my bad habit of neglecting units in figures bit me in the ass for once.

Thanks again. This place is becoming my home away from physics lecture home, I swear.
 

1. How does the given range and angle affect the initial velocity?

The given range and angle determine the initial velocity of an object. The range is the horizontal distance that the object travels, while the angle is the direction of the velocity vector. Both of these values are necessary to calculate the initial velocity of the object.

2. What is the equation for finding the initial velocity with given range and angle?

The equation for finding the initial velocity with given range and angle is:
V₀ = R * √(g/2sinθ)
Where V₀ is the initial velocity, R is the range, g is the gravitational acceleration (9.8 m/s²), and θ is the angle.

3. Can the initial velocity be negative?

Yes, the initial velocity can be negative. This happens when the object is launched in the opposite direction of the positive direction of the coordinate system. In this case, the velocity is considered negative because it is moving in the opposite direction of the positive axis.

4. Is there a specific unit for initial velocity?

The unit for initial velocity depends on the unit of measurement used for the range and angle. For example, if the range is measured in meters and the angle is in degrees, then the initial velocity will be in meters per second (m/s). It is important to use consistent units when calculating the initial velocity.

5. Can the initial velocity be calculated without knowing the time?

Yes, the initial velocity can be calculated without knowing the time. The equation for initial velocity does not include time as a variable, as it only depends on the range and angle. However, the time can be calculated using the initial velocity and other known variables, such as the object's position or acceleration.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
409
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
21
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
974
Back
Top