Question

A boat moves through the water of a river at 4.72 m/s relative to the water, regardless of the boat’s direction. If the current is flowing at 3.86 m/s, how long does it take the boat to complete a trip consisting of a 297 m displacement downstream followed by a 389 m displacement upstream? Answer in units of s.

Answer 1

Answer:

Total time taken by boat to cover all the displacement = 452.3254 sec

Explanation:

We have given speed of boat = 4.72 m/sec

Speed of current flowing = 3.86 m./sec

In downstream relative speed of boat = speed of boat + speed of current flowing = 4.72+3.86 = 8.58 m/sec

Distance traveled downstream = 297 m

So time taken by boat to travel 297 m downstream $t_1=\frac{297}{8.58}=34.615sec$

In upstream relative speed of speed = speed of boat - speed of current flowing = 4.72 -3.86 = 0.86 m/sec

Distance traveled in upstream = 389 m

So time taken to travel 289 m upstream $t_2=\frac{389}{0.86}=452.325sec$

So total time $t=t_1+t_2=34.615+452.325486.94 sec$

Answer 2

Answer:

486.95s

Explanation:

Let the velocity of the boat be $v_b$ and that of the river be $v_r$.

When the boat is moving downstream, the resultant velocity is given by;

$v=v_b+v_r\\Given;\\v_b=4.72m/s\\v_r=3.86m/s\\therefore\\v=4.72m/s+3.86m/s=8.58m/s$

Recall that

$velocity=\frac{dispacement}{time}.............(1)$

Given; downstream displacement, d = 297m. Therefore by equation (1);

$8.58=\frac{297}{t_1}\\t_1=\frac{297}{8.58}\\t_1=34.62s$

where $t_1$ is the time taken to travel downstream displacement.

When the boat is moving upstream it is moving directly against the river current, hence its resultant velocity in this case becomes;

$v=v_b-v_r\\v=4.72-3.86=0.86m/s$

The time taken upstream is then calculated as follows given that the upstream displacement is 389m, according to equation (1);

$0.86=\frac{389}{t_2}$

therefore $t_2=\frac{389}{0.86}=452.326s$

Hence the total time taken by the boat to complete its trip as specified is given as follows;

$t_{total}=t_1+t_2= 34.62+452.326\\t_{total}=486.95s$