Respuesta :
The projectile launch ratios allow finding the velocity for the package to reach the climbers, it must be thrown down with an initial velocity
v_{oy}= 17.52 m / s
given parameters
- Horizontal velocity vₓ = 79.32 m/s
- The height of the plane above the climbers y₀ = 235 m
- The horizontal distance from the plane to the climbers x = 425 m
to find
- vertical initial velocity
Projectile launching is the application of kinematics to motion in two dimensions where there is no acceleration on the x-axis. Let's set a reference frame where the x-axis is in the direction of the plane and the y-axis is vertical and positive upward.
Find the time it takes for the package to reach the climbers
vₓ = [tex]\frac{x}{t}[/tex]
where vₓ is the horizontal velocity, x the displacement and t the time
t = [tex]\frac{x}{v_x}[/tex]
t = 425 / 79.32
t = 5.358 s
This is the time for all movement since time is a scalar
now we look for the initial vertical velocity
y = y₀ + v_{oy} t - ½ g t²
The package is at an initial height of y₀ = 235 m and when it reaches the climbers the height is zero (y = 0)
0 = y₀ + v_{oy} t - ½ g t²
v_{oy} = ½ g t - y₀/ t
v_{oy} = ½ 9.8 5,358 - 235/ 5,368
v_{oy} = 26.2542 - 43.778
v_{oy} = -17.52 m / s
the negative sign indicates that the speed is down
For the package to reach the climbers, it must be thrown downward with an initial velocity of 17.52 m / s.
learn more about projectile launch here:
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