Question

An airplane traveling 1000 m above the ocean at 140 km/h is going to drop a box of supplies to shipwrecked victims below.

(b) What is the horizontal distance between the plane and the victims when the box is dropped?

Answer 1

Horizontal distance = 555.74 m

Step-by-step explanation:

Given the following data;

Height = 1000m

Horizontal velocity = 140km/h

First of all, we would convert the unit of the velocity to meters per seconds;

V = (140 * 1000)/60*60

V = 140000/3600 = 38.89m/s

To find the time, we would use the second equation of motion;

`S = ut + \frac {1}{2}at^(2)`

We know that acceleration due to gravity, g is equal to 9.8m/s²

Initial velocity, u = 0

Substituting into the equation, we have;

`1000 = 0(t) + \frac {1}{2}*9.8*t^(2)`

`1000 = 0 + 4.9*t^(2)`

`1000 = 4.9*t^(2)`

`t^(2) = \frac {1000}{4.9}`

`t = √(204.08)`

Time, t = 14.29 secs

To find the horizontal distance;

Speed = distance/time

`Horizontal \; distance = horizontal \; velocity * time`

`Horizontal \; distance = 38.89 * 14.29`

Horizontal distance = 555.74 m