Answer:
35 m/s down
Explanation:
The horizontal speed of the package is 70 m/s. So the time needed to reach the hikers is:
1000 m / (70 m/s) = 14.28 s
Taking down to be positive, the initial velocity needed is:
Δy = v₀ t + ½ at²
1500 m = v₀ (14.28 s) + ½ (9.8 m/s²) (14.28 s)²
v₀ = 35 m/s
The package must be launched down with an initial velocity of 35 m/s.
Answer: 35 m/s will be the initial vertical launch velocity.
Explanation:
So this is where learning about quadratic equations becomes useful. First we have have to calculate the amount of time it takes the basket to reach the hikers which can be solved by:
1000 m / (70 m/s) = 14.28 s [We know the horizontal displacement and velocity, so calculating time is simple. Convert km to m to make life easier, and remember to handle vertical and horizontal velocity individually.]
The hard part is to find vertical velocity. To do so, set up your equation:
d=v•t+ 1/2 at^2
Vertical displacement we know is 1500 m, time is 14.28s and half acceleration is 4.9m/s^2. Your equation should look like this when the numbers are plugged in:
1500(m)=v•×14.28(s)+4.9(m/s^2)×14.28(s^2)
To convert this into a solvable equation, we will set the left side to 0 and arrange the equation, to look like this:
0=v•14.28(s)+4.9(m/s^2)×14.28(s^2)-1500(m)
Isolate v• and solve.
(Note: v• stands for initial vertical velocity if confused)
