Answer:
The maximum height of the package is 140 m above the ground. Jim Bond will not catch the package.
Explanation:
Hi there!
The equation of height and velocity of the package are the following:
h = h0 + v0 · t + 1/2 · g · t²
v = v0 + g · t
Where:
h = height of the package at time t.
h0 = initial height.
v0 = initial velocity.
t = time.
g = acceleration due to gravity (-9.81 m/s² because we consider the upward direction as positive).
v = velocity of the package at a time t.
First, let´s find the time it takes the package to reach the maximum height. For this, we will use the equation of velocity because we know that at the maximum height, the velocity of the package is zero. So, we have to find the time at which v = 0:
v = v0 + g · t
0 = 50.5 m/s - 9.8 m/s² · t
Solving for t:
-50.5 m/s / -9.81 m/s² = t
t = 5.15 s
Now, let´s find the height that the package reaches in that time using the equation of height. Let´s place the origin of the frame of reference on the ground so that the initial position of the package is 10 m above the ground:
h = h0 + v0 · t + 1/2 · g · t²
h = 10 m + 50.5 m/s · 5.15 s - 1/2 · 9.81 m/s² · (5.15 s)²
h = 140 m
The maximum height of the package is 140 m above the ground. Jim Bond will not catch the package.
