Question

A rubber duck is launched horizontally from the roof of a 32m tall building at a velocity of 8.6 m/s. What is the duck's time of flight? What is the duck's range?

Answer 1

The time of flight of the rubber duck is approximately 2.654 seconds, and its range is approximately 22.92 meters.

Step-by-step explanation:

In projectile motion, the horizontal and vertical motions are independent of each other. The time of flight of the rubber duck can be found using the vertical motion equation:

h = ut + 0.5 * gt^2

Since the duck is launched horizontally, the initial vertical velocity is 0. Therefore, the equation becomes:

h = 0.5 * gt^2

Given that the building is 32m tall, we can substitute the values:

32 = 0.5 * 9.8 * t^2

Solving for t, we get:

t = sqrt(64/9.8) = 2.654s.

The range of the duck can be found using the horizontal motion equation:

r = ut

Since the duck is launched horizontally, the initial horizontal velocity is 8.6 m/s. Therefore, the equation becomes:

r = 8.6 * t

Substituting the value of t, we get:

r = 8.6 * 2.654

≈ 22.92 m.