A plane drops a hamper of medical supplies
from a height of 5750 m during a practice run
over the ocean. The plane’s horizontal velocity was 109 m/s at the instant the hamper
was dropped.
What is the magnitude of the overall velocity of the hamper at the instant it strikes
the surface of the ocean? The acceleration of
gravity is 9.8 m/s
2
.
Answer in units of m/s
V^2 = Vo^2 + 2g*h.
V^2 = 0 + 19.6*5750 = 1127000
V = 1062 m/s.
To find the magnitude of the overall velocity of the hamper at the instant it strikes the surface of the ocean, we can use the principles of projectile motion.
First, let's break down the problem into components:
1. Vertical motion: The hamper is dropped from a height of 5750 m with an initial vertical velocity of 0 m/s. We need to find the final vertical velocity when it reaches the surface of the ocean.
2. Horizontal motion: The hamper has a horizontal velocity of 109 m/s, which remains constant throughout its motion. Horizontal velocity does not affect the vertical motion.
Given that the acceleration due to gravity is 9.8 m/s², we can use the kinematic equation for vertical motion:
v^2 = u^2 + 2as
where:
v = final vertical velocity (unknown)
u = initial vertical velocity (0 m/s)
a = acceleration due to gravity (-9.8 m/s²)
s = vertical displacement (5750 m)
Substituting the values, the equation becomes:
v^2 = 0^2 + 2 * (-9.8) * 5750
Simplifying,
v^2 = 2 * (-9.8) * 5750
v^2 = -113100
Taking the square root of both sides (ignoring the negative solution since velocity cannot be negative in this context),
v ≈ √113100
v ≈ 336.3 m/s
So, the vertical velocity of the hamper when it strikes the surface of the ocean is approximately 336.3 m/s.
To find the magnitude of the overall velocity, we combine the horizontal and vertical velocities using the Pythagorean theorem:
Overall velocity (v) = √(horizontal velocity^2 + vertical velocity^2)
v = √(109^2 + 336.3^2)
v ≈ √(11881 + 112970.69)
v ≈ √124851.69
v ≈ 353.2 m/s
Therefore, the magnitude of the overall velocity of the hamper at the instant it strikes the surface of the ocean is approximately 353.2 m/s.