Projectile motion, finding initial speed

In summary, a projectile fired at an angle of 30° above the horizontal took 2.5 seconds to travel the last 12 meters of its vertical distance and the last 10 meters of its horizontal distance. To find the initial velocity, we first need to find the horizontal velocity, which is 4 m/s. Using the tangent function, we can then find the vertical velocity, which is 2.309 m/s. To find the initial velocity, we use Pythagoras theorem, giving us a final answer of 4.618602 m/s. The problem cannot be solved by finding the initial vertical velocity first because the first equation requires knowledge of the initial velocity or maximum height, which are not given in the problem.
  • #1
vizakenjack
57
4
An object fired at an angle of 30° above the horizontal takes 2.5 s to travel the last 12 m of its vertical distance and the last 10 m of its horizontal distance. With what speed was the object launched? (Note: This problem does not stipulate that the initial and final elevation of the object has to be the same!)

Solution:
First, an initial velocity in x direction (air friction is ignored, I guess, so velocity in x direction stays the same) is to be found.

The object traveled in x direction - 10 meters.
And the formula for horizontal distance is: d = vt
10 = v*2.5s
v = 4m/s
that's the x component of velocity (Vx)

Knowing initial Vx and an angle, we can find the y component of the velocity (Vy)
Tangent is opposite/adjacent. We need to find opposite, which corresponds to Vy.
so: tan(30°) * Vx (adjacent) = Vy
Vy = 2.309 m/s

Now the initial velocity needs to be found. Using Pythagoras theorem: sqrt(4^2 m/s + 2.309^2 m/s) =
4.618602 m/s

The answer is: 4.618602 m/s

But my question is, why doesn't the solution work if instead of finding initial horizontal velocity, initial vertical velocity is to be found first?
See for yourself:
So I see 12 meters is the max height reached by an object, right?
Formula for height in projectile motion is: h = V2y/2g -> 12=V2y/2g
Vy = 15.3362 m/s
It's already wrong!
Why??

I'm also kinda confused whether I should use this formula:
d = V*t + 1/2 * gt2
Anyway, using that kinematic equation yields: 17.05 m/s for Vy
Which is also wrong...
 
Last edited:
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  • #2

I'm not sure, but it seems to me that you are finding the initial velocity in the x direction for a situation where the total horizontal distance is 10. Is that what the problem is asking? It seems to me that the horizontal distance is unknown and you only know the time for the last 10 meters.
 
  • #3
The problem gives distance in both y and x direction.
However, the problem is solvable if you first find the Vx.

Why can't I solve it finding Vy first and then solving for Vx and Velocity?
 
  • #4
The first equation can't be used because it uses the initial velocity to or maximum height to solve it. You have neither those things (hence the note in the problem). The second equation requires knowledge of the initial position in the y direction. Which you also don't have. The values you're given don't qualify.
 
  • #5
Cake said:
The first equation can't be used because it uses the initial velocity to or maximum height to solve it. You have neither those things (hence the note in the problem).don't qualify.
Isn't the "12 m of its vertical distance" = max height reached by an object?

Cake said:
The second equation requires knowledge of the initial position in the y direction. Which you also don't have. The values you're given
Wouldn't the initial y position be 0? Or why can't I assume it's 0?
 
  • #6
vizakenjack said:
Isn't the "12 m of its vertical distance" = max height reached by an object?Wouldn't the initial y position be 0? Or why can't I assume it's 0?
1. No. It doesn't say in the problem that is the max height.
2. No, it tells you this in the note in the problem.
 
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What is projectile motion?

Projectile motion is the motion of an object that is launched or thrown and moves through the air under the influence of gravity.

What is initial speed?

Initial speed, also known as initial velocity, is the speed at which an object is launched or thrown at the beginning of its motion.

How do you calculate initial speed in projectile motion?

To calculate initial speed, you can use the equation v = √(gy/2sinθ), where v is the initial speed, g is the acceleration due to gravity (9.8 m/s²), y is the vertical displacement, and θ is the angle of launch.

What is the importance of finding initial speed in projectile motion?

Finding the initial speed in projectile motion is important because it allows us to predict the trajectory, range, and maximum height of the object. It also helps us understand the motion of objects in real-life scenarios, such as a thrown ball or a launched rocket.

Can initial speed be negative in projectile motion?

Yes, initial speed can be negative in projectile motion if the object is launched at an angle below the horizontal line. This indicates that the object is initially moving downwards.

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