# Thread: Differential Equation Problem Jet Take Off

1. ## 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!

2. 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!
$
\frac{d^2y}{dt^2}= a
$

$
$

$
y=\int{atdt}=at^2/2
$

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

$
\frac{d^2y}{dt^2}= a
$

$
$

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

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

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

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