Solve Physics Problem: Target 120 m Away, Speed 250m/s

  • Thread starter kashmirekat
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In summary, a hunter aiming directly at a target 120 m away with a bullet leaving the gun at a speed of 250m/s on the same level will miss the target by a distance calculated by solving the equation 250t=120 and using that value for t in the equation y= -4.9t2. This is assuming no air resistance.
  • #1
kashmirekat
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1
The question says that a hunter aims directly at a target (on the same level) 120 m away. If the bullet leaves the gun at a speed of 250m/s, by how much will it miss the target?

So my values are v_o=250m/s, r=120m, and angle=0 since they're on the same level, right? And I need to know v to subtract from 120m.

I would just like to know what equation to use, not the answer to the problem. Thank you.
 
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  • #2
The acceleration downward is 9.8 m/s2 so dv/dt= -9.8.
Integrating (or, since this is a constant, just mutiplying)
v= -9.8t+ initial vertical velocity= -9.8t+ 0 so v= dy/dt= -9.8t.
Integrating that, y= -4.9t2+ initial height= -4.9t2.

Neglecting air resistance (which we have to since there is no information on air resistance) there is no horizontal acceleration:
a= dv/dt= 0 so v= initial horizontal velocity= 250 m/s. and then
x= 250t. To go 120 m, requires that 250t= 120. Solve that equation for t and use that t in y= -4.9t2 to find how much the bullet has dropped.
 
  • #3


To solve this physics problem, we can use the equation for horizontal displacement:

Δx = v_o * t

Where Δx is the horizontal displacement, v_o is the initial velocity, and t is the time.

In this case, we know that the initial velocity is 250m/s and the horizontal displacement is 120m. We can rearrange the equation to solve for t:

t = Δx / v_o

Plugging in the values, we get:

t = 120m / 250m/s = 0.48s

Now, we can use the equation for vertical displacement to find the vertical distance the bullet will travel during this time:

Δy = v_o * t + 0.5 * a * t^2

Where Δy is the vertical displacement, v_o is the initial velocity, t is the time, and a is the acceleration (which we can assume to be -9.8m/s^2 for simplicity).

Since we know that the initial vertical velocity is 0m/s (since the bullet is fired horizontally), we can simplify the equation to:

Δy = 0.5 * a * t^2

Plugging in the values, we get:

Δy = 0.5 * (-9.8m/s^2) * (0.48s)^2 = -1.12m

Therefore, the bullet will miss the target by 1.12m. This is because while the bullet is traveling horizontally for 0.48s, it is also falling vertically due to gravity.

I hope this helps and provides you with the necessary equation to solve the problem. Remember to always pay attention to the units and use the appropriate equations for the given situation.
 

1. How do I calculate the time taken for the object to reach the target at 120m away?

To calculate the time taken, we can use the formula t = d/v, where t is the time, d is the distance and v is the velocity. So, in this case, t = 120m/250m/s = 0.48 seconds.

2. Can you explain the concept of projectile motion in this problem?

Projectile motion is the motion of an object that is launched into the air and moves along a curved path due to the influence of gravity. In this problem, the object is launched at a certain angle and speed, and then it follows a parabolic path until it reaches the target 120m away.

3. How can I find the angle at which the object should be launched to hit the target?

To find the angle, we can use the formula θ = tan^-1(y/x), where θ is the angle, y is the vertical distance and x is the horizontal distance. In this problem, y = 120m and x = 120m, so θ = tan^-1(120/120) = 45°. Therefore, the object should be launched at a 45° angle to hit the target.

4. What is the importance of knowing the initial velocity in this problem?

The initial velocity is crucial in determining the trajectory of the object and its final position. Without knowing the initial velocity, we cannot accurately predict the time taken or the angle at which the object should be launched to hit the target.

5. Can this problem be solved using any other formulas or methods?

Yes, there are other formulas and methods that can be used to solve this problem, such as using the equations of motion or using vector analysis. However, the method of using the formula t = d/v and the concept of projectile motion is the most straightforward and efficient way to solve this problem.

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