# Differential Equation Problem Jet Take Off

• Dec 1st 2008, 09:03 PM
ishanj07
Differential Equation Problem Jet Take Off
I really can't figure out this problem nor can i figure a similar problem from an example in class.

Suppose a particular jet needs to attain a speed of 220 mph to take off. If it can accelerate from 0 to 220 mph in 45 seconds, how long must the runway be(in feet)? Assume constant acceleration. Note: 1 mph = 22/15 ft/sec.

Thanks!
• Dec 1st 2008, 10:58 PM
Quote:

Originally Posted by ishanj07
I really can't figure out this problem nor can i figure a similar problem from an example in class.

Suppose a particular jet needs to attain a speed of 220 mph to take off. If it can accelerate from 0 to 220 mph in 45 seconds, how long must the runway be(in feet)? Assume constant acceleration. Note: 1 mph = 22/15 ft/sec.

Thanks!

$\displaystyle \frac{d^2y}{dt^2}= a$
$\displaystyle \frac{dy}{dt}=\int{adt}=at$
$\displaystyle y=\int{atdt}=at^2/2$
hence
$\displaystyle y= \frac{(220-0)*22/15}{45} * {45}^2= ans$
• Dec 2nd 2008, 12:17 AM
mr fantastic
Quote:

$\displaystyle \frac{d^2y}{dt^2}= a$
$\displaystyle \frac{dy}{dt}=\int{adt}=at {\color{red}+ C}$

But dy/dt = 0 when t = 0 therefore C = 0.

$\displaystyle y=\int{atdt}=at^2/2 {\color{red}+ D}$

But y = 0 when t = 0 therefore D = 0.

hence
$\displaystyle y= \frac{(220-0)*22/15}{45} * {45}^2= ans$