Parabolic motion problem: bomber plane case

[thegreengineer]

Ok guys, I got this problem but I don't know how to solve it properly. The problem is about parabolic motion and it says:

A plummeting bomber plane that makes an angle of 53° with the positive y-axis throws a bomb down with a height of 730 m. The bomb impacts the ground 5 s later. a) What was the bomber speed? b) How much distance in the x-axis does the bomb cover in the air? c) What are the components of the velocity just when the bomb hits the ground?

Well before writing down the formulas, I want to say that I got confused because I don't know what kind of motion this is, if it is projectile motion or horizontal projection since we have an angle for the initial velocity. The formulas are most likely to be:

$R_x=\frac{v_{0}^{2}(\mathbf{sin}2\theta)}{g}$
$y_{max}=\frac{v_{0}^{2}(\mathbf{sin}^2\theta)}{2g}$
$\Delta t_f=\frac{2v_0(\mathbf{sin}\theta)}{g}$
$v_x=\left | \mathbf{v} \right |\mathbf{cos}\theta$
$v_y=\left | \mathbf{v} \right |\mathbf{sin}\theta$


I attempted to reach the solutions, however; I'm stuck that I need more data like the initial velocity magnitude as well as the final velocity's so I'm not able to find the time and I cannot find the distance, help please.

 

[mfb]

It is a general motion of an object in free fall.
You can focus on the vertical direction first. An object with an initial height of 730m and an unknown velocity hits the ground 5 seconds later. What was its vertical velocity?

 

[thegreengineer]

That's what I want to find :\

 

[mfb]

Then you should find a formula for the distance traveled as function of the other variables, right?

I will not give you a solution - it is your homework. I can give hints, but you should try to figure it out yourself.

 

[HalfLostAndSearching]

Hello there,

Thank you for sharing your problem with me. It seems like you are on the right track with using the formulas for projectile motion. However, I understand your confusion about whether this is projectile motion or horizontal projection. In this case, it is actually a combination of both.

The bomber plane initially has a vertical velocity component due to its angle of 53° with the positive y-axis, but it also has a horizontal velocity component. This means that the motion of the bomb can be broken down into both projectile motion and horizontal projection.

To solve this problem, we need to use the equations of motion for both projectile motion and horizontal projection. We also need to use the fact that the time of flight for the bomb is 5 seconds.

a) To find the bomber speed, we can use the horizontal projection equation:

v_x = \frac{d}{t}

Where v_x is the horizontal velocity, d is the distance covered in the x-axis, and t is the time of flight. We know that t = 5 seconds, and we can find d by using the projectile motion equation for the maximum height (y_max):

y_{max} = \frac{v_0^2 sin^2\theta}{2g}

We know that y_max = 730 m and we can solve for v_0 by plugging in the values. Once we have v_0, we can use it to find the horizontal velocity component v_x.

b) To find the distance covered in the x-axis, we can use the same equation we used in part a:

d = v_x t

Where d is the distance, v_x is the horizontal velocity we found in part a, and t is the time of flight.

c) To find the components of velocity just when the bomb hits the ground, we can use the final velocity equation for projectile motion:

v_f = v_0 + gt

Where v_f is the final velocity, v_0 is the initial velocity, g is the acceleration due to gravity, and t is the time of flight. We know that t = 5 seconds and we can find v_0 using the equation we used in part a. Once we have v_f, we can break it down into its horizontal and vertical components using the same trigonometric relationships you mentioned in your formulas.

I hope this helps you solve the problem. Remember to always analyze the motion and break it down into its components to make it