Question

Jackson heads east at 25 km/h for 20 minutes before heading south at 45 km/h for 20 minutes. Hunter heads south at 45 km/h for 10 minutes before heading east at 40 km/h for 30 minutes. Find average velocity (magnitude and direction) of each person

Answer 1

Answer:

The average velocity of Jackson is 18.056 m/s South

The average velocity of Hunter is 10.65 m/s East

Explanation:

initial velocity of Jackson, u = 25 km/h east = 6.944 m/s east

time for this motion, $t_i$ = 20 minutes = 1200 seconds

⇒initial displacement of Jackson, $x_i$ = (6.944 m/s) x (1200 s) = 8332.8 m

Final velocity of Jackson, v =  45 km/h South = 12.5 m/s South

time at Jackson's final position, $t_f$ = 20 minutes + $t_i$ = 20 minutes + 20 minutes

time at Jackson's final position, $t_f$ = 40 minutes = 2400 s

⇒Final displacement of Jackson,$x_f$ = (12.5 m/s) x (2400 s) = 30,000m

Average velocity of Jackson;

$= \frac{x_f-x_i}{t_f-t_i} \\\\= \frac{30,000-8332.8}{2400-1200} \\\\= 18.056 \ m/s \ South$

initial velocity of Hunter, u = 45 km/h South = 12.5 m/s South

time for this motion, $t_i$ = 10 minutes = 600 seconds

⇒initial displacement of Hunter, $x_i$ = (12.5 m/s) x (600 s) = 7500 m

Final velocity of Hunter, v =  40 km/h east = 11.11 m/s east

time at Hunter's final position, $t_f$ = 30 minutes + $t_i$ = 30 minutes + 10 minutes

time at Hunter's final position, $t_f$ = 40 minutes = 2400 s

⇒Final displacement of Hunter,$x_f$ = (11.11 m/s) x (2400 s) = 26,664m

Average velocity of Hunter;

$= \frac{x_f-x_i}{t_f-t_o} \\\\= \frac{26,664-7500}{2400-600} \\\\= 10.65 \ m/s \ east$