Projectile Motion Questions: Mechanics for Beginners

[paul9619]

Hi all. I am new to the forum. Mechanics is a totally new subject to me and I have a few questions to post over the next few weeks that i would like your feedback on, just to make sure I am along the right lines :)

The first won i have done is as follows:

1) How is it possible to consider the vertical and horizontal motion of a projectile independently of each other?

I reckon its because the horizontal is constant and has no other force acting in its direction!

2) A Plane of level flight at 300MPH and a height of 4KM drop's a 75KG bomb. Ignoring resistance calculate:

a)The speed of the bomb in meters/sec at the instant of impact

I firstly converted the 300 mph to m/s and got 134.112m/s.
I then used the formula s=ut+1/2at^2 (Vertical elements) to work out the time taken for the bomb to drop. Using s = 4000meters, a = 9.81 m/s. I got 28.56 seconds.

I then used V=u+at and got 0+(9.81x28.56) to give me 280.1736 m/s for the vertical motion.
Then using the formula (root(U^2+V^2)) to get the speed at impact. giving me 310.618 m/s. Is this right for Q2a?

b) Calculate the angle of impact with the ground?

I used the formula: Tan(Theta) = V/U to give me 280.1736/134.112 to give me an angle of 64.42 degrees. The above values being the vertical and horizontal speeds.

c) Calculate the kinetic energy of the bomb at the instant it strikes the ground?

I simply used the formula 1/2mv^2 using m=75KG and v= 310.618 m/s. This gave me 3618.13 Kilo Joules.

Am I along the right lines?
Cheers

 

[Hootenanny]

Hi all. I am new to the forum. Mechanics is a totally new subject to me and I have a few questions to post over the next few weeks that i would like your feedback on, just to make sure I am along the right lines :)

Welcome to the Forums!

1) How is it possible to consider the vertical and horizontal motion of a projectile independently of each other?

I reckon its because the horizontal is constant and has no other force acting in its direction!

What about air resistance? Think perpendicular vectors.

2) A Plane of level flight at 300MPH and a height of 4KM drop's a 75KG bomb. Ignoring resistance calculate:

a)The speed of the bomb in meters/sec at the instant of impact

I firstly converted the 300 mph to m/s and got 134.112m/s.
I then used the formula s=ut+1/2at^2 (Vertical elements) to work out the time taken for the bomb to drop. Using s = 4000meters, a = 9.81 m/s. I got 28.56 seconds.

I then used V=u+at and got 0+(9.81x28.56) to give me 280.1736 m/s for the vertical motion.
Then using the formula (root(U^2+V^2)) to get the speed at impact. giving me 310.618 m/s. Is this right for Q2a?

Your method looks good to me, I'm not checking the math though!

b) Calculate the angle of impact with the ground?

I used the formula: Tan(Theta) = V/U to give me 280.1736/134.112 to give me an angle of 64.42 degrees. The above values being the vertical and horizontal speeds.

Again, your method looks good but I ain't checking your math.

c) Calculate the kinetic energy of the bomb at the instant it strikes the ground?

I simply used the formula 1/2mv^2 using m=75KG and v= 310.618 m/s. This gave me 3618.13 Kilo Joules.

Assuming your answer to (2a) is correct, this is also correct.

 

[paul9619]

What about air resistance? Think perpendicular vectors.

Cheers for the speedy response. The question actually says assume there is no air resistance.

How is it possible to consider the vertical and horizontal motion of a projectile independently of each other?

 

[Hootenanny]

Cheers for the speedy response. The question actually says assume there is no air resistance.

How is it possible to consider the vertical and horizontal motion of a projectile independently of each other?

No problem. However, since perpendicular vectors (and hence forces and accelerations) are independent of each other this Independence would apply even if air resistance would acting.