At a skills competition, a target is being lifted into the air by a cable at a constant speed. An archer standing on the ground
launches an arrow toward the target. The system of equations below models the height, in feet, of the target and the arrow t seconds after it was fired. Which statement most likely describes the situation modeled by this system?
The arrow is fired with an initial upward velocity of 2 ft/s.
The arrow is fired with an initial upward velocity of 4 ft/s.
The arrow is fired with an initial upward velocity of 8 ft/s.
The arrow is fired with an initial
The arrow is fired with an initial upward velocity of 2 ft/s.
The arrow is fired with an initial upward velocity of 4 ft/s.
The arrow is fired with an initial upward velocity of 8 ft/s.
The arrow is fired with an initial
1 answer:
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Answer:
a) The tower is 90 feet tall
b) She reaches the bottom at t = 18 minutes.
c) Her speed at time t is 5 \sqrt[]{5} ft/minute
d) Her acceleration at time t is 10 ft/minute^2
Step-by-step explanation:
Consider the path described by the child as going down the tower to have the following parametrization
a) Assuming that the child is at the top of the tower when she starts going down, we have that at the initial time (t=0) we will have the value of the height of the tower. That is z = 90-5*0 = 90 ft.
b) The child reaches the bottom as soon as z =0. We want to find the value of t that does that. Then we have 0 = 90-5t, which gives us t = 18 minutes.
c) Given the parametrization we are given, the velocity of the child at time t is given by . The speed is defined as the norm of the velocity vector,
so, the speed at time t is given by
d) ON the same fashion we want to know the norm of the second derivative of .
We have that so the acceleration is given by