Samuel travels to the east at 15m/hr for 20 minutes. Then hevtravels 30 degrees north of east 2m/s for 15 minutes. What is his displacement?
Draw the triangle. Distance= sqrt(N^2+E^2)
for the component distances, distance=rate*time in one, you have to conver 20 min to hr, in the the other, convert minutes to seconds.
To find Samuel's displacement, we can break down his motion into two components: the eastward component and the northward component.
First, let's calculate the eastward displacement. Samuel travels at a speed of 15 m/hr for 20 minutes. To convert minutes to hours, we divide 20 by 60:
20 minutes / 60 = 1/3 hour
So, Samuel's eastward displacement is:
Eastward displacement = Speed × Time
= 15 m/hr × 1/3 hr
= 5 meters
Now, let's calculate the northward displacement. Samuel travels 30 degrees north of east at a speed of 2 m/s for 15 minutes. Since the speed is already given in meters per second, we don't need to convert the time.
To calculate the northward displacement, we use trigonometry, specifically finding the vertical component of the velocity. The northward displacement can be found using the formula:
Northward displacement = Speed × Time × sin(angle)
Where the angle is given as 30 degrees.
Northward displacement = 2 m/s × 15 minutes × sin(30 degrees)
= 2 m/s × 15/60 hr × sin(30 degrees)
= 0.5 × 0.25 × 0.5
= 0.0625 meters
Now, to find the total displacement, we use the Pythagorean theorem since the eastward and northward displacements form a right triangle:
Total displacement = √(Eastward displacement^2 + Northward displacement^2)
= √(5^2 + 0.0625^2)
= √(25 + 0.00390625)
≈ √25.00390625
≈ 5 meters (rounded to the nearest meter)
Therefore, Samuel's displacement is approximately 5 meters in magnitude.