A plane is flying horizontally at constant speed, vo. when it releases a package. The package lands on the ground at t seconds later. Just before the package lands...
a. What is its horizontal component of velocity? Leave in terms of vo and t.
b. What is its vertical component of velocity? Leave in terms of vo and t.
c. How would your answers to a and b change if the plane's speed was increased? Explain.
a. vo
b. g*t
a. v*t*cos(theta)
b. v*t*sin(theta)
c. both would increase
a. The horizontal component of velocity remains constant for the package since the plane is flying horizontally. Therefore, its horizontal component of velocity is simply equal to the initial velocity of the plane, vo.
b. The vertical component of velocity of the package just before it lands is equal to the vertical component of velocity it had when it was released. Since the package is released from a horizontally flying plane, there is no initial vertical velocity. Thus, the vertical component of velocity is 0.
c. If the plane's speed is increased, it would have no effect on the horizontal component of velocity of the package just before it lands. This is because, regardless of the plane's speed, the package will always have the same horizontal velocity as the plane.
However, if the plane's speed is increased, it would affect the time it takes for the package to land. As the plane increases its speed, the package would cover a larger horizontal distance in the same amount of time, t. Therefore, the package would take less time to reach the ground.
a. To find the horizontal component of velocity, we need to first understand that the plane is flying horizontally at a constant speed, vo. This means that the horizontal component of velocity remains constant throughout the motion of the package. Therefore, the horizontal component of velocity is also vo.
b. Just before the package lands, the vertical component of velocity is influenced by the force of gravity. Since the package is only affected by gravity vertically, the vertical component of velocity changes over time. To find it, we need to know the time it takes for the package to land, t.
The vertical component of velocity can be determined by the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
In this case, the package starts with an initial vertical velocity of 0, as it was released from rest. The acceleration due to gravity, a, is approximately -9.8 m/s², directed downwards. Therefore, the equation becomes:
v = 0 + (-9.8)t
v = -9.8t
So, the vertical component of velocity just before the package lands is -9.8t.
c. If the plane's speed is increased, only the horizontal component of velocity would change. The vertical component of velocity is determined solely by the acceleration due to gravity and the time the package takes to land, t. It is not affected by the horizontal speed of the plane.
Therefore, increasing the plane's speed (changing vo) would only impact the horizontal component of velocity (a). The vertical component of velocity (b) would remain the same.