• Support PF! Buy your school textbooks, materials and every day products Here!

Kinematics of a falling object to hit target

  • #1

Homework Statement


An airplane flies horizontally with a speed of 300m/s at an altitude of 300m. Assume the ground is level. At what horizontal distance from a target must the pilot release a bomb as to hit the target?

Answer: 2.7km

Homework Equations


a=v/t=d/t2
r_f = r_i + v_i*t + 1/2at2

The Attempt at a Solution


I tried approaching this question using a kinematics equation and just the basic a=v/t approach...

a=v/t=d/t2
t = sqrt( 2 * d / g ) = 9s
d(horizontal) = vt = (300)(9) = 2.7km

r_f = r_i + v_i*t + 1/2at2
Using the quadratic equation to find t = 62.5s
d(horizontal) = (300)(62.5) = 18.7km

Why can I not use the kinematics equation to approach this problem?
In general, how do I know whether its appropriate to approach a problem using kinematics vs. the "basic" equations (a=v/t; v=d/t)?
 

Answers and Replies

  • #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,796
1,667

Homework Statement


An airplane flies horizontally with a speed of 300m/s at an altitude of 300m. Assume the ground is level. At what horizontal distance from a target must the pilot release a bomb as to hit the target?

Answer: 2.7km

Homework Equations


a=v/t=d/t2
r_f = r_i + v_i*t + 1/2at2

The Attempt at a Solution


I tried approaching this question using a kinematics equation and just the basic a=v/t approach...

a=v/t=d/t2
t = sqrt( 2 * d / g ) = 9s
d(horizontal) = vt = (300)(9) = 2.7km

r_f = r_i + v_i*t + 1/2at2
Using the quadratic equation to find t = 62.5s
d(horizontal) = (300)(62.5) = 18.7km

Why can I not use the kinematics equation to approach this problem?
In general, how do I know whether its appropriate to approach a problem using kinematics vs. the "basic" equations (a=v/t; v=d/t)?
For one thing, the vertical velocity of the bomb is not constant, so how do you calculate a = v/t?

And another thing. You haven't calculated the correct free-fall time of this bomb when it is dropped from an altitude of 300 m. Check your arithmetic again.
 
  • #3
For one thing, the vertical velocity of the bomb is not constant, so how do you calculate a = v/t?

And another thing. You haven't calculated the correct free-fall time of this bomb when it is dropped from an altitude of 300 m. Check your arithmetic again.
A bit of a typo, but I meant that the altitude was 400m. Either way, you're right I wasn't calculating it correctly.
First off, I realized that the initial velocity of the bomb is 0m/s. Just because its being dropped from a moving plane, free fall is independent of how it starts falling.

r_f = r_i +v_i*t + 1/2at2
0 = 400 - 4.9t2
400=-4.9t2
t = 9 seconds to for the bomb to reach the ground.

300m/s * 9 seconds = 2.7km
I multiplied these because the plane is going to move an "extra" 300m for every second.
 
  • #4
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,503
5,435
I multiplied these because the plane is going to move an "extra" 300m for every second.
More to the point, the bomb continues forwards at 300m each second.

To answer your question about when you can use certain equations, the only general kinematics equations involve integrals and derivatives. The SUVAT equations can be deduced from those when acceleration is constant. That includes a=v/t (or more accurately, ##a=\Delta v/\Delta t##). But v=d/t is only valid when there is no acceleration.
 

Related Threads on Kinematics of a falling object to hit target

Replies
2
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
536
  • Last Post
Replies
2
Views
1K
Replies
17
Views
3K
  • Last Post
2
Replies
31
Views
4K
  • Last Post
Replies
2
Views
3K
Replies
1
Views
900
Replies
1
Views
1K
Replies
3
Views
3K
Top