Question

example (do this one yourself)
a student wants to airdrop a food parcel to the stranded person on the island:

• draw the trajectory of the food parcel
• calculate the time to land
• calculate where she should release the parcel.

practice problems

1. on the diagrams below, draw vectors showing:

the acceleration (left diagram)
the total velocity
the vertical component of velocity
the horizontal component of velocity

1. a boy and girl are climbing a tree. the girl is 10 m above the ground and throws a ball horizontally at 18 ms^{-1}. the boy is 12 m above the ground and can only throw her ball horizontally at 15 ms^{-1}. whose ball lands furthest from the tree?

Explanation:

Identify given values

We analyze the "EXAMPLE (DO THIS ONE YOURSELF)" problem.

• Initial horizontal velocity: \(u_x = 100\text{ m s}^{-1}\)
• Initial vertical velocity: \(u_y = 0\text{ m s}^{-1}\)
• Vertical displacement: \(s_y = -500\text{ m}\) (downward)
• Acceleration due to gravity: \(g = 9.8\text{ m s}^{-2}\) (downward)

Calculate time to land

We use the vertical motion equation:

$$s_y = u_y t + \frac{1}{2} a_y t^2$$

Since \(u_y = 0\) and \(a_y = -g\):

$$-500 = -\frac{1}{2} (9.8) t^2$$

$$t^2 = \frac{1000}{9.8} \approx 102.04$$

$$t \approx 10.1\text{ s}$$

Calculate release position

We find the horizontal distance traveled during flight:

$$s_x = u_x t$$

$$s_x = 100 \times 10.1 = 1010\text{ m}$$

The parcel must be released \(1010\text{ m}\) horizontally before reaching the island.

Answer:

• Trajectory: A parabolic curve starting from the plane and curving downwards to the stranded person on the island.
• Time to land: \(10.1\text{ s}\) (using \(g = 9.8\text{ m s}^{-2}\)) or \(10.0\text{ s}\) (if using \(g = 10\text{ m s}^{-2}\)).
• Release position: \(1010\text{ m}\) horizontally before the island (or \(1000\text{ m}\) if using \(g = 10\text{ m s}^{-2}\)).