Projectile Motion AP Physics

Question

A plane drops a hamper of medical supplies from a height of 3620 m during a practice run over the ocean. The plane’s horizontal velocity was 107 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.

Answer 1

The velocity as the hamper hits the water has 2 components or pieces, its velocity in the x direction and its velocity in the y direction. In the x-direction it was 107 m/s at time t=0 and it will be 107 m/s all the way down until it hits the water (there is no force in the x direction so it doesn't change). For the velocity in the y direction, it acts just like an object in free fall that is dropped from a height of 3620 meters. At t=0 its y-direction velocity is 0. Then it picks up speed as it goes down due to the force of gravity. The associated kinematic equation is v_f² = v_i² + 2a_y(y_f - y_i) where v_f is the final velocity, v_i is the initial velocity, a_y is the acceleration in the y direction (or g) and (y_f - y_i) is the change in y distance (3620 meters)

So v_f² = 0² + 2(9.8)(3620) = 70952

Taking the square root gives v_f = 266.37 m/s

Now we have the horizontal velocity as 107 m/s ad the vertical velocity as 266.37 m/s like this:

To find the magnitude of the final overall velocity we use the Pythagorean Theorem to solve for the hypotenuse of the triangle (the red dotted line) which is the resultant vector.

Vel = square root (107² + 266.37²) = 287.06 m/s

Since we used 2 sig figs in g, we should really round to two sig figs but your teacher may wish you to consider 9.8 as a standard that doesn't count in which case you would use 3 sig figs from the other two givens to make the magnitude of the final vel = 287 m/s