Question

Two cruise ships leave port at the same time. Ship A sails north at a speed of 20 mph while Ship B sails east at a speed of 40 mph.
(a) Find an expression in terms of the time t (in hours) giving the distance D between two ships.
D(t) =



(b) Using the expression obtained in part (a), find the distance between the two ships 4 hr after leaving the port. (Round your answer to two decimal places.)
mi

Answer 1

Answer:

a) D(t) = $\[20*\sqrt{5} * t\]$

b) 178.885 miles

Step-by-step explanation:

Ship A travels north at the rate of 20 mph.

Ship B travels east at the rate of 40 mph.

After t hours, Ship A is at a distance of 20t miles from the origin.

Similarly, Ship B is at a distance of 40t miles from the origin.

(a) Distance D(t) = $\[\sqrt{(20t)^{2}+(40t)^{2}}\]$

= $\[\sqrt{400*t^{2}+1600 * (t)^{2}}\]$

= $\[\sqrt{2000*t^{2}}\]$

= $\[20*\sqrt{5} * t\]$

(b) Distance between the two ships when t = 4,

= $\[20*\sqrt{5} * 4\]$

= $\[80*\sqrt{5} \]$ miles

= 80 * 2.236

= 178.885 miles