A plane drops hamper of medical supplies from a height of 2740m during a practice run over the ocean. The plane's horizontal velocity was 126m/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 9.8m/s^2.
Answer in units of 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 break down the problem into two components: vertical and horizontal.

First, let's calculate the time it takes for the hamper to fall to the surface of the ocean. We can use the equation:

h = (1/2) * g * t^2

Where:
h is the height (2740m)
g is the acceleration due to gravity (9.8 m/s^2)
t is the time

Rearranging the equation, we get:

t^2 = (2 * h) / g

Plugging in the values, we have:

t^2 = (2 * 2740m) / (9.8m/s^2)

Calculating this, t^2 is approximately 558.37s^2. Taking the square root of this will give us the time it takes for the hamper to fall:

t = sqrt(558.37s^2) ≈ 23.64s

Now, let's calculate the horizontal distance the hamper travels during this time. We can use the equation:

d = v * t

Where:
d is the horizontal distance
v is the horizontal velocity of the plane (126m/s)
t is the time (23.64s)

Plugging in the values, we have:

d = 126m/s * 23.64s

Calculating this, the horizontal distance is approximately 2988.64m.

Since velocity is a vector quantity, we can calculate the overall velocity using a vector addition of the horizontal and vertical velocities.

The horizontal velocity remains constant at 126m/s, so the horizontal component of the overall velocity will also be 126m/s.

For the vertical component, we can calculate it using the equation of motion:

v = u + at

Where:
v is the final velocity (unknown)
u is the initial velocity (0m/s, as it was dropped)
a is the acceleration due to gravity (-9.8m/s^2, as it acts downwards)
t is the time (23.64s)

Plugging in the values, we have:

v = 0m/s + (-9.8m/s^2) * 23.64s ≈ -231.672m/s

The negative sign indicates that the velocity is in the opposite direction to the positive y-axis (upwards).

Now, we can find the magnitude of the overall velocity by using the Pythagorean theorem:

Overall Velocity = √(Horizontal Velocity^2 + Vertical Velocity^2)

Plugging in the values, we have:

Overall Velocity = √(126m/s)^2 + (-231.672m/s)^2)

Calculating this, the magnitude of the overall velocity of the hamper at the instant it strikes the surface of the ocean is approximately 264.76 m/s.

The vertical velocity component, after impact from height H, is sqrt(2*g*H)

H = 2740 m in this case.

The horizontal velocity component is 126 m/s

Use the Pythagorean Theorem for the speed (velocity magnitude).