A plane drops a hamper of medical supplies from a height of 2960m during a practice run over the ocean. The planes horizontal velocity was 108m/s at the instant the hamper was dropped. What is the magnitude of the overall velocity at the hamper at the instant it strikes the surface of the ocean. The acceleration of gravity is 9.8m/s^2. Answer in units of m/s.
To find the magnitude of the overall velocity at the instant the hamper strikes the surface of the ocean, we can use the concept of vector addition.
The horizontal velocity remains constant throughout the motion, so the horizontal component of velocity at the instant of impact is still 108 m/s.
To find the vertical component of velocity, we can use the equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity (unknown)
u = initial velocity (vertical component)
a = acceleration due to gravity (-9.8 m/s^2, taking downward as positive)
s = displacement in the vertical direction (-2960 m)
We can rearrange the equation to solve for the final velocity:
v^2 = u^2 + 2as
v^2 = 0^2 + 2(-9.8)(-2960)
v^2 = 2(9.8)(2960)
v^2 = 57760
Taking the square root of both sides gives us:
v = √57760
v ≈ 240.4 m/s
Therefore, the magnitude of the overall velocity at the instant the hamper strikes the surface of the ocean is approximately 240.4 m/s.
To find the magnitude of the overall velocity of the hamper at the instant it strikes the surface of the ocean, we need to break down the velocity into its horizontal and vertical components.
Given:
Initial vertical height (h) = 2960 m
Horizontal velocity (Vx) = 108 m/s
Acceleration due to gravity (g) = 9.8 m/s²
First, let's determine the time it takes for the hamper to reach the surface by using the vertical motion equation:
h = (1/2)gt²
Rearranging the equation, we have:
t² = (2h) / g
t² = (2 * 2960) / 9.8
t ≈ 24.183 seconds
Now let's find the vertical velocity (Vy) at the instant the hamper hits the surface. We can use the equation:
Vy = gt
Vy = 9.8 m/s² * 24.183 s
Vy ≈ 237.548 m/s (upward)
The horizontal velocity (Vx) remains constant since there is no horizontal acceleration. Therefore, the horizontal velocity when the hamper strikes the surface is the same as the initial horizontal velocity:
Vx = 108 m/s
Now we can find the resultant velocity (V) at the instant the hamper strikes the surface by using the Pythagorean theorem:
V² = Vx² + Vy²
V² = (108 m/s)² + (237.548 m/s)²
V² = 11664 m²/s² + 56403.290 m²/s²
V² ≈ 68067.290 m²/s²
V ≈ √68067.290 m²/s²
V ≈ 261.049 m/s
Therefore, the magnitude of the overall velocity at the instant the hamper strikes the surface of the ocean is approximately 261.049 m/s.