They're both going 7.5 miles per second but 1 hour and 30 minutes apart. So the closest time together is 12:00 PM because at 9:30 + 2:50, because that is how far apart they are, which equals 12:00 PM.
Here:
Closest at 12:00 PM
Distance is 2.5 m/s
One ship, sailing east with a speed of 7.5 m/s, passes a certain point at 8A.Mand a second ship sailing north at the same speed, passed the same point at 9:30 A.M. At What time are they closest together and what is the distance between them then?
4 answers
let a be the distance from a to the ship1
and b be the distance from a to the ship2
now c is the distance between a and b.
c^2=a^2+b^2
let time t be the time after 8AM, so t=0 is 8 am, 9:30 is 1.5
I am going to use speed 7, you can do it yourself with speed 7.5
c^2=(7*t )^2 + (7(t-1.5))^2
c^2=49(t^2+t^2-3t+2.25)
taking the derivative and setting dc/dt=0, then
0=49(4t-3)
time t=3/4 hr or 45 min.
and at that time,
c=7*sqrt(18/16-9/4+2.25)=7.42
check this.
and b be the distance from a to the ship2
now c is the distance between a and b.
c^2=a^2+b^2
let time t be the time after 8AM, so t=0 is 8 am, 9:30 is 1.5
I am going to use speed 7, you can do it yourself with speed 7.5
c^2=(7*t )^2 + (7(t-1.5))^2
c^2=49(t^2+t^2-3t+2.25)
taking the derivative and setting dc/dt=0, then
0=49(4t-3)
time t=3/4 hr or 45 min.
and at that time,
c=7*sqrt(18/16-9/4+2.25)=7.42
check this.
They are closest at 8:45 am and the distance between them is 28637.82m
JEE mains ka bhi dijyena sir