Question

A hummingbird 3.4m above the ground flies 1.2 m along a straight line path. Upon spotting a flower below, the hummingbird drops directly downward 1.4m to hover in front of the flower. What is the hummingbirds total displacement

Answer 1

Answer:

1.84m, 49.4⁰ South west

Explanation:

Step 1: construct a right angled triangle from the birds displacement

⇒From the diagram uploaded; we calculate the resultant/total displacement (R) of the bird using Pythagoras theorem.

R² = 1.2² + 1.4²

R² = 3.4

R = √3.4

R = 1.84 m

Step 2: calculate the direction of the bird's displacement

From vector diagram head-to-tail rule, we determine the cardinal direction;

From the diagram; $tan(\alpha) = \frac{1.4}{1.2}$

$tan(\alpha) = 1.1667$

$\alpha =tan^{-1} 1.1667$

$\alpha = 49.4^o$

Therefore the hummingbirds total displacement is 1.84m, 49.4⁰ South west

Answer 2

A = horizontal displacement of the humming bird = 1.2 m

B = vertical displacement of the humming bird = 1.4 m

C = net displacement of the humming bird from initial to final position = ?

In the triangle drawn , Using Pythagorean theorem

C = √(A² + B²)

inserting the values

C = √(1.2² + 1.4²)

C = √(1.44 + 1.96)

C = √(3.4)

C = 1.4 m

Hence the net displacement of hummingbird comes out to be 1.4 m