Question

1. a student is on the southern bank of a river that is 36m wide and has current with a velocity of 6.2m/s w. she needs to get directly across the river and decides to pint the motor of the boat due north. the motor has push the boat with a speed of 2.0m/s. (10 marks)

a) how long does it take the student to get across the river?
b) what is the resultant velocity of the boat?
c) when the student lands on the opposite bank, how far is she from her destination?

Explanation:

Assume the river flows east (perpendicular to north-south bank for direct crossing; correction: boat velocity is north, current is east/west? Wait—direct crossing needs boat velocity component opposite current, but problem says boat pushed due north (2.0m/s), current is 0.2m/s (typo: "6.2m/s [W]" is likely 0.2m/s west? Wait no—original says current velocity 6.2m/s [W]? Wait river width 36m, boat speed north 2.0m/s.

Step1: Time to cross (north direction)

Time = width / north velocity
$t = \frac{36}{2.0} = 18s$

Step2: Resultant velocity magnitude

Current west: $v_x=6.2m/s$, north: $v_y=2.0m/s$
$v_{res} = \sqrt{v_x^2 + v_y^2} = \sqrt{6.2^2 + 2.0^2} = \sqrt{38.44 + 4} = \sqrt{42.44} \approx 6.51m/s$

Step3: Drift distance west

Drift = current speed × time
$d = 6.2×18 = 111.6m$

Answer:

A) 18s
B) ~6.5m/s
C) 111.6m

(Note: Assuming current is west (perpendicular to north boat direction); if "6.2m/s [W]" was a typo, e.g., 0.2m/s, drift would be 3.6m, but following given number: 6.2m/s west.)